RS Agarwal Solution | Class 10th | Chapter-17 | Volumes and Surface Areas of Solids | Edugrown

Exercise Ex. 17A

Question 1

Two cubes each of volume 27 cm’ are joined end to end to form a solid. Find the surface area of the resulting cuboid.Solution 1

Question 2

Solution 2

Question 3

If the total surface area of a solid hemisphere is 462 cm², find its volume.Solution 3

Question 4

A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs. 25 per metre.Solution 4

Question 5

If the volumes of two cones are in the ratio of 1: 4 and their diameters are in the ratio of 4 : 5, find the ratio of their heights.Solution 5

Question 6

The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km². Find the height of the mountain.Solution 6

Question 7

The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq metres, find its volume.Solution 7

Question 8

The surface area of a sphere is 2464 cm². If its radius be doubled, what will be the surface area of the new sphere?Solution 8

Question 9

A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 in surmounted by a right circular cone of same base radius. Find the length of canvas used in making the tent, if the breadth of the canvas is 1.5 m.Solution 9

s 

Question 10

A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs.80 per square meter. Take Solution 10

Radius of the cylinder = 14 m

And its height = 3 m

Radius of cone = 14 m

And its height = 10.5 m

Let l be the slant height

Curved surface area of tent

                    = (curved area of cylinder + curved surface area of cone)

Hence, the curved surface area of the tent = 1034 

Cost of canvas = Rs.(1034 × 80) = Rs. 82720Question 11

A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, find the area of canvas needed to make the tent. Take .Solution 11

For the cylindrical portion, we have radius = 52.5 m and height = 3 m

For the conical portion, we have radius = 52.5 m

And slant height = 53 m

Area of canvas = 2rh + rl = r(2h + l)

Question 12

A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius of the cylinder is 2.5m, its height of 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.Solution 12

Radius o f cylinder = 2.5 m

Height of cylinder = 21 m

Slant height of cone = 8 m

Radius of cone = 2.5 m

Total surface area of the rocket = (curved surface area of cone

                                                              + curved surface area of cylinder + area of base)

Question 13

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.Solution 13

Question 14

A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.Solution 14

Height of cone = h = 24 cm

Its radius = 7 cm

Total surface area of toy

Question 15

A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm³ and its diameter is 7 cm, find the height of the toy.Solution 15

Question 16

A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the ice-cream cone.Solution 16

Question 17

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Find its capacity.Solution 17

Radius of hemisphere = 10.5 cm

Height of cylinder = (14.5 10.5) cm = 4 cm

Radius of cylinder = 10.5 cm

Capacity = Volume of cylinder + Volume of hemisphere

Question 18

A toy is in the form of a cylinder with hemispherical ends. If the whole length of the toy is 90 cm and its diameter is 42 cm, find the cost of painting the toy at the rate of 70 paise per sq cm.Solution 18

Question 19

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.Solution 19

Question 20

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, find the total surface area of the article when it is ready.

Solution 20

Height of cylinder = 20 cm

And diameter = 7 cm and then radius = 3.5 cm

Total surface area of article

               = (lateral surface of cylinder with r = 3.5 cm and h = 20 cm)

Question 21

A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 21. cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and its height is 9.8 cm, find the volume of the water left in the tub.Solution 21

Radius of cylinder 

And height of cylinder 

Radius of cone r = 2.1 cm

And height of cone 

Volume of water left in tub

              = (volume of cylindrical tub – volume of solid)

Question 22

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8cm and of base radius 6 cm, is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid. Take = 3.14Solution 22

(i)Radius of cylinder = 6 cm

Height of cylinder = 8 cm

Volume of cylinder

Volume of cone removed

(ii)Surface area of cylinder = 2 = 2× 6 × 8 

Question 23

From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.Solution 23

Question 24

From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid.Solution 24

Question 25

Solution 25

Question 26

A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold. Use = .Solution 26

Diameter of spherical part of vessel = 21 cm

Question 27

The adjoining figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volume of the solid.

Solution 27

Height of cylinder = 6.5 cm

Height of cone = 

Radius of cylinder = radius of cone

                          = radius of hemisphere

                         = 

Volume of solid = Volume of cylinder + Volume of cone

+ Volume of hemisphere

Question 28

From a cubical piece of wood of side 21 cm, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece. Find the surface area and volume of the remaining piece.Solution 28

Question 29

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs.5 per 100 sq cm. [Use π = 3.14.]Solution 29

Question 30

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.Solution 30

Question 31

The inner diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is 16 cm, find the apparent capacity and the actual capacity of the glass.

Solution 31

Question 32

A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours.

Solution 32

Exercise Ex. 17B

Question 1

The dimensions of a metallic cuboid are 100 cm x 80 cm x 64 cm. It is melted and recast into a cube. Find the surface area of the cube.Solution 1

Question 2

A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.Solution 2

Question 3

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.Solution 3

Question 4

A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. Find the number of balls thus formed.Solution 4

Radius of the cone = 12 cm and its height = 24 cm

Volume of cone = 

Question 5

The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.Solution 5

Question 6

The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.Solution 6

Internal radius = 3 cm and external radius = 5 cm

Hence, height of the cone = 4 cmQuestion 7

A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m. Find the Thickness of the wire.Solution 7

Question 8

A hemispherical bowl of internal diameter 30cm contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl.Solution 8

Inner radius of the bowl = 15 cm

Volume of liquid in it = 

Radius of each cylindrical bottle = 2.5 cm and its height = 6 cm

Volume of each cylindrical bottle

Required number of bottles = 

   Hence, bottles required = 60Question 9

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.Solution 9

Radius of the sphere= 

Let the number of cones formed be n, then

            Hence, number of cones formed = 504Question 10

A spherical cannon ball 28 cm in diameter is melted and recast into right circular conical mould, base of which is 35 cm in diameter. Find the height of the cone.Solution 10

Radius of the cannon ball = 14 cm

Volume of cannon ball = 

Radius of the cone = 

Let the height of cone be h cm

Volume of cone = 

            Hence, height of the cone = 35.84 cmQuestion 11

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5cm and 2 cm. Find the radius of third ball.Solution 11

Let the radius of the third ball be r cm, then,

           Volume of third ball = Volume of spherical ball volume of 2 small balls

Question 12

A spherical shell of lead whose external and internal diameters are respectively 24 cm and 18 cm, is melted ad recast into a right circular cylinder 37 cm high. Find the diameter of the base of the cylinder.Solution 12

External radius of shell = 12 cm and internal radius = 9 cm

Volume of lead in the shell = 

Let the radius of the cylinder be r cm

Its height = 37 cm

Volume of cylinder = 

Hence diameter of the base of the cylinder = 12 cmQuestion 13

A hemisphere of lead of radius 9 cm is cast intoa right circular cone of height 72 cm. Find the radius of the base of the cone.Solution 13

Volume of hemisphere of radius 9 cm

Volume of circular cone (height = 72 cm)

Volume of cone = Volume of hemisphere

Hence radius of the base of the cone = 4.5 cmQuestion 14

A spherical ball of diameter 21 cm is melted and recast into cubes, each of side 1 cm. Find the number of cubes so formed.Solution 14

Diameter of sphere = 21 cm

Hence, radius of sphere = 

Volume of sphere =  = 

Volume of cube = a³ = (1 1 1) 

Let number of cubes formed be n

Volume of sphere = n Volume of cube

Hence, number of cubes is 4851.Question 15

How many lead balls, each of radius 1 cm, can be made from a sphere of radius 8 cm?Solution 15

Volume of sphere (when r = 1 cm) =  = 

Volume of sphere (when r = 8 cm) =  = 

Let the number of balls = n

Question 16

A solid sphere of radius 3cm is melted and then cast into small spherical balls, each of diameter 0.6 cm. Find the number of small balls so obtained.Solution 16

Radius of sphere = 3 cm

Volume of sphere = 

Radius of small sphere = 

Volume of small sphere = 

Let number of small balls be n

Hence, the number of small balls = 1000.Question 17

The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.Solution 17

Diameter of sphere = 42 cm

Radius of sphere = 

Volume of sphere = 

Diameter of cylindrical wire = 2.8 cm

Radius of cylindrical wire = 

Volume of cylindrical wire = 

Volume of cylindrical wire = volume of sphere

Hence length of the wire 63 m.Question 18

The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.Solution 18

Diameter of sphere = 18 cm

Radius of copper sphere = 

Length of wire = 108 m = 10800 cm

Let the radius of wire be r cm

But the volume of wire = Volume of sphere

Hence the diameter = 2r = (0.3 2) cm = 0.6 cmQuestion 19

A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied into a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel.Solution 19

Question 20

Solution 20

Question 21

The rain water from a roof of 44 m x 20 m drains into a cylindrical tank having diameter of base 4 m and height 3.5 m. If the tank is just full, find the rainfall in cm.Solution 21

Question 22

Solution 22

Question 23

A solid right circular cone of height 60 cm and radius 30 cm is dropped in a right circular cylinder full of water, of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder, in cubic metres.Solution 23

Question 24

Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in level of water in the tank in half an hour.Solution 24

Question 25

Water is flowing at the rate of 6 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 60 m long and 22 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.Solution 25

Question 26

Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/hr. How much area will it irrigate in 10 minutes if 8 cm of standing water is needed for irrigation?Solution 26

Question 27

A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/h, in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate ofRs. 0.07. use Solution 27

Height of cylindrical tank = 2.5 m

Its diameter = 12 m, Radius = 6 m

Volume of tank = 

Water is flowing at the rate of 3.6 km/ hr = 3600 m/hr

Diameter of pipe = 25 cm, radius = 0.125 m

Volume of water flowing per hour

Question 28

Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minute. Find the rate of flow of water in the pipe in km/hr.Solution 28

Question 29

150 spherical marbles, each of diameter 14 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.Solution 29

Question 30

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.Solution 30

Let the number of marbles be n

n volume of marble = volume of rising water in beaker

Question 31

In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?Solution 31

Question 32

In a corner of a rectangular field with dimensions 35 m x 22 m, a well with 14 m inside diameter is dug 8 m deep. The earth dug out is spread evenly over the remaining part of the field. Find the rise in the level of the field.Solution 32

Question 33

A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cu-cm, find the weight of the wire.Solution 33

Question 34

A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of it as found appropriate)Solution 34

Exercise Ex. 17C

Question 1

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 16 cm and 12 cm. Find the capacity of the glass.Solution 1

Question 2

The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area. [Use π = 3.14.]Solution 2

Question 3

A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find

(i) the volume of water which can completely fill the bucket;

(ii) the area of the metal sheet used to make the bucket.Solution 3

Question 4

A container, open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs. 21 per litre.Solution 4

Question 5

A container, open at the top and made up of metal sheet, is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the cost of metal sheet used to make the container, if it costs Rs. 10 per 100 cm².Solution 5

Question 6

The radii of the circular ends of a solid frustum of a cone are 33cm and 27 cm, and its slant height is 10 cm. Find its capacity and total surface area. Take .Solution 6

Here R = 33 cm, r = 27 cm and l = 10 cm

Capacity of the frustum 

Total surface area = 

Question 7

A bucket is in the form of a frustum of a cone. Its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm, respectively. Find how many litres of water can the bucket hold. Take Solution 7

Height = 15 cm, R =  and  

Capacity of the bucket = 

Quantity of water in bucket = 28.49 litresQuestion 8

A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs. 15 per . Use Solution 8

R = 20 cm, r = 8 cm and h = 16 cm

Total surface area of container = 

Cost of metal sheet used = Question 9

A bucket made up of a metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs. 20 per litre and the cost of metal sheet used if it costs Rs. 10 per 100Solution 9

R = 15 cm, r = 5 cm and h = 24 cm

(i)Volume of bucket = 

Cost of milk = Rs. (8.164 20) = Rs. 163.28

(ii)Total surface area of the bucket

Cost of sheet = Question 10

A container in the shape of a frustum of a cone having diameters of its two circular faces as 35 cm and 30 cm and vertical height 14 cm, is completely filled with oil. If each cm’ of oil has mass 1.2 g, then find the cost of oil in the container if it costs Rs.40 per kg.Solution 10

Question 11

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket.Solution 11

Question 12

The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm < 14). If the volume of bucket is 5390 cm³, find the value of r.Solution 12

Question 13

The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area. [Use π = 3.14.]Solution 13

Question 14

A tent is made in the form of a frustum of a cone surmounted by another cone. The diameters of the base and the top of the frustum are 20 m and 6 m respectively, and the height is 24 m. If the height of the tent is 28 m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required. Take Solution 14

R = 10cm, r = 3 m and h = 24 m

Let l be the slant height of the frustum, then

Quantity of canvas = (Lateral surface area of the frustum)

                                + (lateral surface area of the cone)

Question 15

A tent consists of a frustum of a cone, surmounted by a cone. If the diameters of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12mm, find the area of the canvas required to make the tent. (Assume that the radii of the upper circular ends of the frustum and the base of the surmounted conical portion are equal.)Solution 15

ABCD is the frustum in which upper and lower radii are EB = 7 m and FD = 13 m

Height of frustum= 8 m

Slant height of frustum

Radius of the cone = EB = 7 m

Slant height of cone = 12 m

Surface area of canvas required

Question 16

The perimeters of the two circular ends of a frustum of a cone are 48 cm and 36 cm. If the height of the frustum is 11 cm, find its volume and curved surface area.Solution 16

Question 17

A solid cone of base radius 10 cm is cut into two parts through the midpoint of its height, by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

Solution 20

Question 21

An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet requited to make the funnel.

Solution 21

Exercise Ex. 17D

Question 1

A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km/hr. Find the amount of water (in cubic metres) that runs into the sea per minute.Solution 1

Question 2

The volume of a cube is 729 cm³. Find its surface area.Solution 2

Question 3

How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?Solution 3

Question 4

Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. Find the edge of the new cube formed.Solution 4

Question 5

Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.Solution 5

Question 6

The volumes of two cubes are in the ratio 8 : 27. Find the ratio of their surface areas.Solution 6

Question 7

Solution 7

Question 8

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 cm³, find the radius of the base of the cylinder.Solution 8

Question 9

The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Find the ratio of their volumes.Solution 9

Question 10

66 cubic cm of silver is drawn into a wire 1 mm in diameter. Calculate the length of the wire in metres.Solution 10

Question 11

If the area of the base of a right circular cone is 3850 cm² and its height is 84 cm, find the slant height of the cone.Solution 11

Question 12

A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. Calculate the radius of the base of the cone.Solution 12

Question 13

A right cylindrical vessel is full of water. How many right cones having the same radius and height as those of the right cylinder will be needed to store that water?Solution 13

Question 14

The volume of a sphere is 4851 cm³. Find its curved surface area.Solution 14

Question 15

The curved surface area of a sphere is 5544 cm³. Find its volume.Solution 15

Question 16

The surface areas of two spheres are in the ratio of 4 : 25. Find the ratio of their volumes.Solution 16

Question 17

A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. Find the number of spherical balls obtained.Solution 17

Question 18

How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm x 11 cm x 12 cm?Solution 18

Question 19

A metallic cone of radius 12 cm and height 24 cm is melted and made into spheres of radius 2 cm each. How many spheres are formed?Solution 19

Question 20

A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Find the radius of the base of the cone.Solution 20

Question 21

A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.Solution 21

Question 22

The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm respectively. Find the slant height of the frustum.Solution 22

Question 23

Find the ratio of the volume of a cube to that of a sphere which will fit inside it.Solution 23

Question 24

Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?Solution 24

Question 25

Two cubes each of volume 125 cm³ are joined end to end to form a solid. Find the surface area of the resulting cuboid.Solution 25

Question 26

Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed.Solution 26

Question 27

A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, find its width.Solution 27

Question 28

A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used, at the rate of Rs. 25 per metre.Solution 28

Question 29

A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the volume of wood in the toy.Solution 29

Question 30

Solution 30

Question 31

A hollow sphere of external and internal diameters 8 cm and 4 cm respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone.Solution 31

Question 32

A bucket of height 24 cm is in the form of frustum of a cone whose circular ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of Rs. 30 per litre, which the bucket can hold.Solution 32

Question 33

The interior of a building is in the form of a right circular cylinder of diameter 4.2 m and height 4 m surmounted by a cone of same diameter. The height of the cone is 2.8 m. Find the outer surface area of the building.Solution 33

Question 34

A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find the diameter of the sphere.Solution 34

Question 35

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.Solution 35

Question 36

If the radii of the circular ends of a bucket 28 cm high, are 28 cm and 7 cm, find its capacity and total surface area.Solution 36

Question 37

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm³ of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket. (Useπ = 3.14.)Solution 37

Question 38

The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs.1.40 per cm².Solution 38

Question 39

Solution 39

Question 40

A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of water

(i) displaced out of the cylinder

(ii) left in the cylinder.Solution 40

Exercise MCQ

Question 1

Choose the correct answer in each of the following:

A cylindrical pencil sharpened at one edge is the

combination of

(a) a cylinder and a cone

(b) a cylinder and frustum of a cone

(c) a cylinder and a hemisphere

(d) two cylindersSolution 1

Correct option: (a)

A cylindrical pencil sharpened at one edge is the combination of a cylinder and a cone. Observe the figure, the lower portion is a cylinder and the upper tapering portion is a cone.Question 2

A shuttlecock used for playing badminton is the combination of

(a) cylinder and a hemisphere

(b) frustum of a cone and a hemisphere

(c) a cone and a hemisphere

(d) a cylinder and a sphere

Solution 2

Correct option: (b)

A shuttlecock used for playing badminton is the combination of a frustum of a cone and a hemisphere, the lower portion being the hemisphere and the portion above that being the frustum of the cone.Question 3

A funnel is the combination of

(a) a cylinder and a cone

(b) a cylinder and a hemisphere

(c) a cylinder and frustum of a cone

(d) a cone and a hemisphere

Solution 3

Correct option: (c)

A funnel is the combination of a cylinder and frustum of a cone. The lower portion is cylindrical and the upper portion is a frustum of a cone.Question 4

A surahi is a combination of

(a) a sphere and a cylinder

(b) a hemisphere and a cylinder

(c) a cylinder and a cone

(d) two hemispheres Surahi

Solution 4

Correct option: (a)

A surahi is a combination of a sphere and a cylinder, the lower portion is the sphere and the upper portion is the cylinder.Question 5

The shape of a glass (tumbler) is usually in the form of

(a) a cylinder

(b) frustum of a cone

(c) a cone

(d) a sphere Glass

Solution 5

Correct option: (b)

The shape of a glass (tumbler) is usually in the form of a frustum of a cone.Question 6

The shape of a gill in the gilli-danda game is a combination of

(a) a cone and a cylinder

(b) two cylinders Gilli

(c) two cones and a cylinder

(d) two cylinders and a cone

Solution 6

Correct option: (c)

The shape of a gill in the gilli-danda game is a combination of two cones and a cylinder. The cones at either ends with the cylinder in the middle.Question 7

A plumbline (sahul) is the combination of

(a) a hemisphere and a cone

(b) a cylinder and a cone

(c) a cylinder and frustum of a cone

(d) a cylinder and a sphere Plumbline

Solution 7

Correct option: (a)

A plumbline (sahul) is the combination of a hemisphere and a cone, the hemisphere being on top and the lower portion being the cone.Question 8

A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left over is called

(a) a cone

(b) a sphere

(c) a cylinder

(d) frustum of a cone

Solution 8

Correct option: (d)

A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left over is called the frustum of a cone.Question 9

During conversion of a solid from one shape to another, the volume of the new shape will

(a) decrease

(b) increase

(c) remain unaltered

(d) be doubledSolution 9

Correct option: (c)

During conversion of a solid from one shape to another, the volume of the new shape will remain altered.Question 10

In a right circular cone, the cross section made by a plane parallel to the base is a

(a) sphere

(b) hemisphere

(c) circle

(d) a semicircleSolution 10

Correct option: (c)

In a right circular cone, the cross section made by a plane parallel to the base is a circle.Question 11

A solid piece of iron in the form of a cuboid of dimensions (cccm) is moulded to form a solid sphere. The radius of the sphere is

(a) 19 cm

(b) 21 cm

(c) 23 cm

(d) 25 cmSolution 11

Question 12

The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is

(a) 2.1

(b) 4.2

(c) 8.4

(d) 1.05Solution 12

Question 13

A metallic solid sphere of radius 9 cm is melted to form a solid cylinder of radius 9 cm. The height of the cylinder is

(a) 12 cm

(b) 18 cm

(c) 36 cm

(d) 96 cmSolution 13

Question 14

A rectangular sheet of paper 40 cm × 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is,

Solution 14

Question 15

The number of solid spheres, each of diameter 6 cm, that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is

(a) 2

(b) 4

(c) 5

(d) 6Solution 15

Question 16

The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is

(a) 64 : 27

(b) 16:9

(c) 4 :3

(d) 16³ : 9³Solution 16

Question 17

If the surface area of a sphere is 616 cm², its diameter (in cm) is

(a) 7

(b) 14

(c) 28

(d) 56Solution 17

Question 18

If the radius of a sphere becomes 3 times then its volume will become

(a) 3 times

(b) 6 times

(c) 9 times

(d) 27 timesSolution 18

Question 19

If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm then its slant height is

Solution 19

Question 20

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises by

(a) 3 cm

(b) 4 cm

(c) 5 cm

(d) 6 cmSolution 20

Question 21

A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is  

(a) 1 : 2

(b) 1 : 4

(c) 1 : 6

(d) 1 : 8Solution 21

Question 22

The radii of the circular ends of a bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the bucket is

(a) 41

(b) 43

(c) 49

(d) 51Solution 22

Question 23

A solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal then the ratio of its radius and the slant height of the conical part is

(a) 1 : 2

(b) 2 : 1

(c) 1 : 4

(d) 4 : 1Solution 23

Question 24

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a) 1 : 2

(b) 2 : 1

(c) 1 : 4

(d) 4: 1Solution 24

Question 25

A cubical ice-cream brick of edge 22 cm is to be distributed among some children by filling ice-cream cones of radius 2 cm and height 7 cm up to its brim. How many children will get the ice-cream cones?

(a) 163

(b) 263

(c) 363

(d) 463Solution 25

Question 26

(a) 11000

(b) 11100

(c) 11200

(d) 11300Solution 26

Question 27

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

(a) 2 cm

(b) 3 cm

(c) 4 cm

(d) 6 cmSolution 27

Question 28

The diameters of two circular ends of a bucket are 44 cm and 24 cm, and the height of the bucket is 35 cm. The capacity of the bucket is

(a) 31.7 litres

(b) 32.7 litres

(c) 33.7 litres

(d) 34.7 litresSolution 28

Question 29

The slant height of a bucket is 45 cm and the radii of its top and bottom are 28 cm and 7 cm respectively. The curved surface area of the bucket is

(a) 4953 cm²

(b) 4952 cm²

(c) 4951 cm²

(d) 4950 cm²Solution 29

Question 30

The volumes of two spheres are in the ratio 64:27. The ratio of their surface area is

(a) 9:16

(b) 16:9

(c) 3:4

(d) 4:3Solution 30

Question 31

(a) 142296

(b) 142396

(c) 142496

(d) 142596Solution 31

Question 32

A metallic spherical shell of internal and external diameters 4 cm and 8 cm respectively, is melted and recast into the form of a cone of base diameter 8 cm. The height of the cone is

(a) 12 cm

(b) 14 cm

(c) 15 cm

(d) 8 cmSolution 32

Question 33

A medicine capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of the entire capsule is 2 cm. The capacity of the capsule is 

(a) 0.33 cm³

(b) 0.34 cm³

(c) 0.35 cm³

(d) 0.36 cm³Solution 33

Question 34

The length of the longest pole that can be kept in a room (12 m × 9 m × 8 m) is

(a) 29 m

(b) 21 m

(c) 19 m

(d) 17 mSolution 34

Question 35

Solution 35

Question 36

The volume of a cube is 2744 cm³. Its surface area is

(a) 196 cm²

(b) 1176 cm²

(c) 784 cm²

(d) 588 cm²Solution 36

Question 37

The total surface area of a cube is 864 cm². Its volume is

(a) 3456 cm³

(b) 432 cm³

(c) 1728 cm³

(d) 3456 cm³Solution 37

Question 38

How many bricks each measuring (25 cm × 11.25 cm × 6 cm) will be required to construct a wall (8 m × 6 m × 22.5 cm)?

(a) 8000

(b) 6400

(c) 4800

(d) 7200Solution 38

Question 39

The area of the base of a rectangular tank is 6500 cm² and the volume of water contained in it is 2.6 m³. The depth of water in the tank is.

(a) 3.5 m

(b) 4 m

(c) 5 m

(d) 8 mSolution 39

Question 40

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 m³. The breadth of the wall is

(a) 30 cm

(b) 40 cm

(c) 22.5 cm

(d) 25 cmSolution 40

Question 41

If the areas of three adjacent faces of a cuboid are x, y, z respectively then the volume of the cuboid is

Solution 41

Question 42

(a) 361 cm²

(b) 125 cm²

(c) 236 cm²

(d) 486 cm²Solution 42

Question 43

If each edge of a cube is increased by 50%, the percentage increase in the surface area is

(a) 50%

(b) 75%

(c) 100%

(d) 125%Solution 43

Question 44

How many bags of grain can be stored in a cuboidal granary (8 m× 6m × 3 m), if each bag occupies a space of 0.64 m³?

(a) 8256

(b) 90

(c) 212

(d) 225Solution 44

Question 45

A cube of side 6 cm is cut into a number of cubes each of side 2 cm. The number of cubes formed is

(a) 6

(b) 9

(c) 12

(d) 27Solution 45

Question 46

In a shower, 5 cm of rain falls. The volume of the water that falls on 2 hectares of ground, is

(a) 100 m³

(b) 10 m³

(c) 1000 m³

(d) 10000 m³Solution 46

Question 47

Two cubes have their volumes in the ratio 1: 27. The ratio of their surface areas is

(a) 1 : 3

(b) 1 : 8

(c) 1 : 9

(d) 1 : 18Solution 47

Question 48

The diameter of the base of a cylinder is 4 cm and its height is 14 cm. The volume of the cylinder is

(a) 176 cm³

(b) 196 cm³

(c) 276 cm³

(d) 352 cm³Solution 48

Question 49

The diameter of a cylinder is 28 cm and its height is 20 cm. The total surface area of the cylinder is

(a) 2993 cm²

(b) 2992 cm²

(c) 2292 cm²

(d) 2229 cm²Solution 49

Question 50

The height of a cylinder is 14 cm and its curved surface area is 264 cm². The volume of the cylinder is

(a) 308 cm³

(b) 396 cm³

(c) 1232 cm³

(d) 1848 cm³Solution 50

Question 51

The curved surface area of a cylinder is 1760 cm² and its base radius is 14 cm. The height of the cylinder is

(a) 10 cm

(b) 15 cm

(c) 20 cm

(d) 40 cmSolution 51

Question 52

The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is

(a) 2 :1

(b) 3:1

(c) 4:1

(d) 5:1Solution 52

Question 53

The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. The height of the pillar is

(a) 4 m

(b) 5 m

(c) 6 m

(d) 7 mSolution 53

Question 54

The ratio between the radius of the base and the height of the cylinder is 2 : 3. If its volume is 1617 cm³, the total surface area of the cylinder is

(a) 308 cm²

(b) 462 cm²

(c) 540 cm²

(d) 770 cm²Solution 54

Question 55

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5 : 3. The ratio of their volumes is

(a) 27 : 20

(b) 20 : 27

(c) 4 :9

(d) 9 : 4Solution 55

Question 56

Two circular cylinders of equal volume have their heights in the ratio 1:2. The ratio of their radii is

Solution 56

Question 57

The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is

Solution 57

Question 58

The diameter of the base of a cone is 42 cm and its volume is 12936 cm³. Its height is

(a) 28 cm

(b) 21 cm

(c) 35 cm

(d) 14 cmSolution 58

Question 59

The area of the base of a right circular cone is 154 cm² and its height is 14 cm. Its curved surface area is

Solution 59

Question 60

On increasing each of the radius of the base and the height of a cone by 20% its volume will be increased by

(a) 20%

(b) 40%

(c) 60%

(d) 72.8%Solution 60

Question 61

The radii of the base of a cylinder and a cone are in the ratio 3:4. If they have their heights in the ratio 2 : 3, the ratio between their volumes is

(a) 9 :8

(b) 3:4

(c) 8 :9

(d) 4 : 3Solution 61

Question 62

A metallic cylinder of radius 8 cm and height 2 cm is melted and converted into a right circular cone of height 6 cm. The radius of the base of this cone is

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 8 cmSolution 62

Question 63

The height of a conical tent is 14 m and its floor area is 346.5 m². How much canvas, 1.1 m wide, will be required for it?

(a) 490 m

(b) 525 m

(c) 665 m

(d) 860 mSolution 63

Question 64

The diameter of a sphere is 14 cm. Its volume is

Solution 64

Question 65

The ratio between the volumes of two spheres is 8: 27. What is the ratio between their surface areas?

(a) 2:3

(b) 4:5

(c) 5:6

(d) 4: 9Solution 65

Question 66

A hollow metallic sphere with external diameter 8 cm and internal diameter 4 cm is melted and moulded into a cone having base radius 8 cm. The height of the cone is

(a) 12 cm

(b) 14 cm

(c) 15 cm

(d) 18 cmSolution 66

Question 67

A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is

(a) 2.1 cm

(b) 1.05 cm

(c) 1.5 cm

(d) 2 cmSolution 67Question 68

The volume of a hemisphere is 19404 cm³. The total surface area of the hemisphere is

(a) 4158 cm²

(b) 16632 cm²

(c) 8316 cm²

(d) 3696 cm²Solution 68

Correct option: (a)

Question 69

The surface area of a sphere is 154 cm². The volume of the sphere is all

Solution 69

Correct option: (a)

Question 70

The total surface area of a hemisphere of radius 7 cm is

(588 𝜋) cm²

(392 𝜋) cm²

(147 𝜋) cm²

(598 𝜋) cm²Solution 70

Question 71

The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm. Its volume is

(a) 60060 cm³

(b) 80080 cm³

(c) 70040 cm³

(d) 80160 cm³Solution 71

Question 72

If the radii of the ends of a bucket are 5 cm and 15 cm and it is 24 cm high then its surface area is

(a) 1815.3 cm²

(b) 1711.3 cm²

(c) 2025.3 cm²

(d) 2360 cm²Solution 72

Question 73

A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of canvas required is

(a) 1760 m²

(b) 2640 m²

(c) 3960 m²

(d) 7920 m²Solution 73

Question 74

Match the following columns:

Column I	Column II
A solid metallic sphere of radius 8 cm is melted and the material is used to make solid right cones with height 4 cm and radius of the base 8 cm. How many cones are formed?	(p) 18
A 20-in-deep well with diameter 14 m is dug up and the earth from digging is evenly spread out to form a platform 44 m by 14 in. The height of the platform is …… m.	(q) 8
A sphere of radius 6 cm is melted and recast into the shape of a cylinder of radius 4 cm. Then, the height of the cylinder is…… cm.	(r) 16 : 9
The volumes of two spheres are in the ratio 64: 27. The ratio of their surface areas is …..	(s) 5

The correct answer is

(a)-….., (b)- ….. , (c)- ….., (d)- ……Solution 74

Question 75

Match the following columns:

Column I	Column II
The radii of the circular ends of a bucket in the form of frustum of a cone of height 30 cm are 20 cm and 10 cm respectively. The capacity of the bucket is …….cm3.	(p) 2418 π
The radii of the circular ends of a conical bucket of height 15 cm are 20 cm and 12 cm respectively. The slant height of the bucket is… cm.	(q) 22000
The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. The total surface area of the bucket is …cm2.	(r) 12
Three solid metallic spheres of radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The diameter of the resulting sphere is ….cm.	(s) 17

The correct answer is

(a)-….., (b)- ….. , (c)- ….., (d)- ……Solution 75

Question 76

Assertional- and-Resons type

Each question consists of two statements, namely,

Assertion (A) and Reason (R). For selecting the correct

answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

Assertion (A)	Reason (R)
If the radii of the circular ends of a bucket 24 cm high are 15 cm and 5 cm respectively, then the surface area of the bucket is 545π cm2.	If the radii of the circular ends of the frustum of a cone are R and r respectively and its height is h, then its surface area is π (R2 + r2 + l(R-r), Where l2 = h2+(R-r)2

The correct answer is (a)/(b)/(c) /(d) .Solution 76

Question 77

Assertional- and-Resons type

Each question consists of two statements, namely,

Assertion (A) and Reason (R). For selecting the correct

answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

Assertion (A)	Reason (R)
A hemisphere of radius 7 cm is to be painted outside on the surface. The total cost of painting at it Rs. 5 per cm2 is Rs. 2300.	The total surface area hemisphere is 3πr2.

The correct answer is (a)/(b)/(c) /(d) .Solution 77

Question 78

Assertional- and-Resons type

Each question consists of two statements, namely,

Assertion (A) and Reason (R). For selecting the correct

answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

Assertion (A)	Reason (R)
The number of coins 1.75 cm in diameter and 2 mm thick from a melted cuboid (10 cm× 5.5 cm × 3.5 cm) is 400.	Volume of a cylinder of base radius r and height h is given byV = (πr2h) cubic units.And, area of a cuboid= (l × b × h) cubic units.

The correct answer is (a)/(b)/(c) /(d) .Solution 78

Question 79

Assertional- and-Resons type

Each question consists of two statements, namely,

Assertion (A) and Reason (R). For selecting the correct

answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

Assertion (A)	Reason (R)
If the volumes of two spheres are in the ratio 27:8 then their surface areas are in the ratio 3:2.

The correct answer is (a)/(b)/(c) /(d) .Solution 79

Question 80

Assertional- and-Resons type

Each question consists of two statements, namely,

Assertion (A) and Reason (R). For selecting the correct

answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

Assertion (A)	Reason (R)
The curved surface area of a cone of base radius 3 cm and height 4cm is (15π) cm2.	Volume of a cone = πr2h.

The correct answer is (a)/(b)/(c) /(d) .Solution 80

Exercise FA

Question 1

Find the number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metallic cylinder of height 45 cm and diameter 4 cm.Solution 1

Question 2

Two right circular cylinders of equal volumes have their heights in the ratio 1: 2. What is the ratio of their radii?Solution 2

Question 3

A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, find the total area of the canvas required.Solution 3

Question 4

The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm respectively. Find the curved surface area of the bucket.Solution 4

Question 5

A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. Find the number of balls formed.Solution 5

Question 6

A hemispherical bowl of internal diameter 30 cm is full of a liquid. This liquid is filled into cylindrical-shaped bottles each of diameter 5 cm and height 6 cm. How many bottles are required?Solution 6

Question 7

A solid metallic sphere of diameter 21 cm is melted and recast into Milan cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.Solution 7

Question 8

The diameter of a sphere is 42 cm. it is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.Solution 8

Question 9

A drinking glass is in the shape of frustum of a cone of height 21 cm with 6 cm and 4 cm as the diameters of its two circular ends. Find the capacity of the glass.Solution 9

Question 10

Two cubes, each of volume 64 cm³, are joined end to end. Find the total surface area of the resulting cuboid.Solution 10

Question 11

Solution 11

Question 12

A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.Solution 12

Question 13

A hemispherical bowl of internal radius 9 cm is full of water. This water is to be filled in cylindrical bottles of diameter 3 cm and height 4 cm. Find the number of bottles needed to fill the whole water of the bowl.Solution 13

Question 14

Solution 14

Question 15

The slant height of the frustum of a cone is 4 cm and the perimeters (i.e., circumferences) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.Solution 15

Question 16

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each hemispherical end is 7 cm, find the surface area of the solid.Solution 16

Question 17

From a solid cylinder whose height is 15 cm and diameter 16 cm, a conical cavity of the same height and same “diameter is hollowed out. Find the total surface area of the remaining solid. (Use 𝜋 = 3.14.)Solution 17

Question 18

A solid rectangular block of dimensions 4.4 m, 2.6 in and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.Solution 18

Question 19

An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket. Also, find the volume of water the bucket can hold, in litres.Solution 19

Question 20

A fanner connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km/hr, in how much time will the tank be filled completely?Solution 20