Chapter 19 – Surface Areas and Volume of a Circular Cylinder Exercise Ex. 19.1

Question 1Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, find its height.

Solution 1

Question 2In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.Solution 2 Height (h) of cylindrical pipe = Length of cylindrical pipe = 28 m
  Radius (r) of circular end of pipe =  cm = 2.5 cm = 0.025 m
  CSA of cylindrical pipe =  = 4.4 
    Thus, the area of radiating surface of the system is 4.4 m² or 44000 cm².

Question 3A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs.12.50 per m².Solution 3Height of the pillar = 3.5 m
Radius of the circular end of the pillar = cm = 25 cm  = 0.25 m
CSA of pillar =  = 
Cost of painting 1  area = Rs 12.50
Cost of painting 5.5  area = Rs (5.5 12.50) = Rs 68.75

Thus, the cost of painting the CSA of pillar is Rs 68.75.

Question 4It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet are required for the same?   Solution 4Height (h) of cylindrical tank = 1 m.
    Base radius (r) of cylindrical tank =  = 70 cm = 0.7 m
Area of sheet required = total surface area of tank = 

So, it will require 7.48 of metal sheet.

Question 5

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Question 6

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Question 7

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Question 8

The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find (i)    Its inner curved surface area,
 (ii)    The cost of plastering this curved surface at the rate of Rs 40 per m²

Solution 8Inner radius (r) of circular well = 1.75 m
Depth (h) of circular well = 10 m (i) Inner curved surface area = 

          = (44 x 0.25 x 10) 
          = 110 m²(ii) Cost of plastering 1 m² area = Rs 40                    
    Cost of plastering 110 m² area = Rs (110 x 40) = Rs 4400

Question 9The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?   Solution 9Radius of circular end of cylindrical penholder = 3 cm
Height of penholder = 10.5 cm
Surface area of 1 penholder = CSA of penholder + Area of base of     SA of 1 penholder =  + 
Area of cardboard sheet used by 1 competitor = 
    Area of cardboard sheet used by 35 competitors
 = 7920 cm2
    Thus, 7920 cm² of cardboard sheet will be required for the competition.

Question 10

Solution 10

Question 11

Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of Rs 2.50 per square metre?Solution 11

Question 12

Solution 12

Question 13

The total surface area of a hollow metal cylinder open at both ends of external radius 8 cm and height 10 cm is 338 cm². Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.Solution 13

Question 14

Find the lateral or curved surface area of a cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high. How much steel was actually used, if  of the steel actually used was wasted in making the closed tank?Solution 14Height (h) cylindrical tank = 4.5 m
Radius (r) of circular end of cylindrical tank =m = 2.1m
    (i)    Lateral or curved surface area of tank = 
                                    = 
                                    = 59.4 m2            

    (ii)    Total surface area of tank = 2 (r + h)
              = 
              = 87.12 m²

    Let A m² steel sheet be actually used in making the tank.


Thus, 95.04  steel was used in actual while making the tank.    

Chapter 19 – Surface Areas and Volume of a Circular Cylinder Exercise Ex. 19.2

Question 1A soft drink is available in two packs –

(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and(ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?   Solution 1The tin can will be cuboidal in shape.Length (l) of tin can = 5 cm
Breadth (b) of tin can = 4 cm
Height (h) of tin can = 15 cm
Capacity of tin can = l  b  h = (5  4  15) cm³ = 300 cm³Radius (R) of circular end of plastic cylinder = Height (H) of plastic cylinder = 10 cmCapacity of plastic cylinder = R²H  ==385 cm³Thus, the plastic cylinder has greater capacity.
Difference in capacity = (385 – 300) cm³ = 85 cm³

Question 2The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10m. How much concrete mixture would be required to build 14 such pillars?

Solution 2

Question 3The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. find the mass of the pipe, if 1 cm³ of wood has a mass of 0.6 g.Solution 3

Question 4If the lateral surface of a cylinder is 94.2 cm² and its height is 5 cm, then find
(i) radius of its base    (ii) its volume. (Use  = 3.14)Solution 4(i)    Height (h) of cylinder = 5 cm
        Let radius of cylinder be r.
        CSA of cylinder = 94.2 cm²
        2rh = 94.2 cm²
        (2  3.14  r  5) cm = 94.2 cm²
        r = 3 cm (ii)    Volume of cylinder = r²h = (3.14  (3)² 5) cm³ = 141.3 cm³

Question 5The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?Solution 5Let radius of the circular ends of the cylinder be r.
Height (h) of the cylindrical vessel = 1 m
Volume of cylindrical vessel = 15.4 litres = 0.0154 m³

Total  Surface area of vessel = 2 r(r+h)

                                            Thus, 0.4708 m² of metal sheet would be needed to make the cylindrical vessel.   Question 6A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?Solution 6Radius (r) of cylindrical bowl = cm = 3.5 cm
Height (h) up to which the bowl is filled with soup = 4 cmVolume of soup in 1 bowl = r²h= 
Volume of soup in 250 bowls = (250  154) cm³ = 38500 cm³ = 38.5 litres

Thus, the hospital will have to prepare 38.5 litres of soup daily to serve 250 patients.

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Question 8

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Question 9

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Question 10

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Question 11

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Question 12

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Question 13

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Question 14

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Question 15

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Question 16

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Question 17

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Question 18

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Question 19

A cylinderical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32 cm x 22 cm x 14 cm. Find the rise in the level of the water when the solid is completely submerged.Solution 19

Question 20

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Question 21

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Question 22

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Question 23

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Question 24

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Question 25

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Question 26

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Question 27

A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to around it to a width of 21 m to form an embankment. Find the height of the embankment.Solution 27

Question 28

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Question 29

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per second into cylindrical tank. The water is collected in a cylindrical vessel radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?Solution 29

Question 30

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Question 31

The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m². Find the volume of the cylinder.Solution 31

Question 32A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.Solution 32