1.) Assertion: If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.

Reason : Curved surface area is increased when diameter decreases

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c) Assertion is correct but reason is false

2) Assertion: The volume and surface Area of a sphere are related to each other by radius.

Reason : Relation between Surface Area S and Volume V is `S^(3) = 36 pi V^(2)`.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

3) Assertion: The external dimensions of a wooden box are 18 cm, 10 cm and 6 cm respectively and thickness of the wood is 15 mm, then the internal volume is 765 cm3.

Reason : If external dimensions of a rectangular box be l, b and h and the thickness of its sides be x , then its internal volume is (l – 2x) (b – 2x) (h – 2x)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

4) Assertion: The radius of a cylinder is doubled and its height remaining same. Then its volume will be increased four times.

Reason (R): Volume of the cylinder is πr^2h where, r = radius of base and h = height of the cylinder.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

5) Assertion: The surface area of a sphere is 2464 . Then its volume is 11498(2/3)cm^3

Reason (R): The volume of a sphere of radius 4/3πr^3 is , and total surface area is 4πr^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: b)  both Assertion and reason are correct but reason is not correct explanation for Assertion

6) Assertion: Volume of sphere=4/3πr^3 and surface area of sphere=4πr^2

Reason: if the volume of two sphere are in the ratio27:8 then the surface area are in the ratio 3:2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c) assertion is correct but reason is false

7) Assertion: total surface area of cylinder having radius of the base 14cm and height 30 cm is 3872cm^2

Reason: if r be the radius and h be the height of the cylinder then the total surface area= (2πrh+2πr^2)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

8) Assertion: the slant height of the frustum of a cone is 5 cm and the difference between the radii of its two circular ends is 4 cm than the height of the frustum is 3 cm

Reason: slant height of frustum of cone is given by l= √(R-r)^2+h^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

9) Assertion: if r be the radius and h be the slant height of cone then the slant height =√(h^2+r^2)

Reason: if the height of cone is 24 cm and diameter of base is 14cm then the slant height of cone is 15 cm

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c)  Assertion is  correct but reason is  false

10) Assertion: total surface area of cuboid is 2(lb+bh+lh)

Reason: two identical solid cube of side 5 cm are joined end to end then the total surface area of the resulting cuboid is 300 cm^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c)  Assertion is  correct but reason is  false

11) Assertion: volumes of cone =1/3πr^2h

Reason: the radii of two cone are in the ratio 2:3 and their volumes in the ratio 1:3 then the ratio of their height is 3:2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c)  Assertion is  correct but reason is  false

12) Assertion: if a ball is in the shape of a sphere has a surface area of 221.76cm^2 then  it’s diameter is 8.4 cm

Reason: if the radius of the sphere be r then the surface area, S=4πr^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

13) Assertion: the number of cins 1.75 cm in diameter and 2mm thick is formed from a melted cuboid 10cm*5.5cm*3.5cm is 400

Reason: volume of cylinder= πr^2h cubic units and area of cuboid =(l*b*h) cubic units

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

14) Assertion: number of spherical balls that can be made out of a solid cube lead whose edge 44 cm each ball being 4 cm in diameter is 2541

Reason: number of balls = volume of one ball/ volume of lead

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c) Assertion is correct but reason is false

15) Assertion: volume of sphere =4/3πr^3 and it’s surface area 4πr^2

Reason: if the volumes of two spheres are in the ratio 27:8 then their surface area are in ratio 9:4

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

16) Assertion: total surface area of hemisphere is 3πr^2

Reason: the outer surface of hemisphere of radius 7cm is to be painted the total cost of painting atvrs 5 per cm^2is RS 2300

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c) Assertion is correct but reason is false

17) Assertion: the curved surface area of a cone base radius 3 cm and height 4cm is 15πcm^2

Reason: curved surface area  of a cone = πr^2h

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c)Assertion is correct but reason is false.

18) Assertion: 5 number of solid sphere each of diameter 6 cm that could be moulded to form a solid metallic cylinder of height 45 cm and diameter 4 cm

Reason: number of solid sphere = volume of cylinder / volume of sphere.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

19) Assertion: two circular cylinder of equal volumes have their height in the ratio 1:2 then ratio of their radii is √2:1

Reason. releation between the height and radius of volume is inversely proportional.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

20) Assertion: the number of coins 1.75 cm  in diameter 2 mm thick from a melted cuboid (10cm*5.5cm*3.5cm) is500

Reason: volume of cylinder base and radius r and height h is given by V= πr^2hcubic units

and volume of cuboid=(l+b+h)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertionc) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: d) both Assertion and reason are false

21) Assertion: a closed cylindrical tank of radius 7  m and height 3 m is made from metal 440m^2 sheet of  metal is required.

Reason: surface area of cylinder= 2πr(r+h)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

22) Assertion: the volume and surface area of a sphere are related to each other by radius.

Reason: the relation between the surface area and volume is S^3=36V^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

23) Assertion: the volume of a solid is defined as the space occupied by the solid shape in 3-dimesional region

Reason: the amount of water the glass can hold is called volume of glass

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

24) Assertion: in a cylinder radius is doubled and height is halved  curved surface area will be same

Reason : curved surface area of cylinder= 2πRH

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

25) Assertion: if a ball shape of a sphere has surface area 221.76cm^2 then it’s diameter is 8.4cm

Reason: if the radius of sphere be r then the surface area , S=4πr^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

26) Assertion: curved surface of cylinder= 2πrh

Reason:  if the curved surface ofright circular cylinder  1760cm^2 and it’s radius is 21cm then it’s height is 80/3 cm

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c) Assertionis correct but reason is false

27) Assertion: 220cm^2 the curved surface area of a right circular cone whose slant height

is 10 cm and base radius is 7 cm.

Reason: Curved surface area = πrl

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

28) Assertion: The point of intersection of the 3 edges of a cuboid is called the vertex of a cuboid

Reason:  a cuboid has 8 vertices.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation Assertion

29) Assertion: The volume of a solid is equal to the product of the base area and its height

Reason: Volume = (Length × Breadth × Height)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion

30) Assertion: a cone is solid figure

Reason: a cone is generated when rectangular sheet is rotated about its axis

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c) Assertion is true but reason is false.

31) Assertion: the radii of two cones are in the ratio 2:3 and their height are in ratio 7:3 the ratio of their volumes is 28:27

Reason: volume of cone=1/2πr^2h

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c) Assertion is true but reason is false

32) Assertion: √1400 is the maximum length of rod that can be kept in cuboidal box of sides 30 cm ,20 cm and 10 cm

Reason: diagonal is the longest length in the cuboid

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

33) Assertion: the surface area of cube whose edge equal S to 3 cm is 54sq.cm

Reason: surface area of cube

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

34) Assertion: the surface area of cuboid shaped box having  length80cm,breadth40cm,height20cm is 11200

Reason: surface are of box= 2(ll+bb+hh)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c) Assertion is true but reason is false

35) Assertion: if the radius of cylinder is 4 cm and height 10 cm then the total surface area of cylinder is 352sq.cm

Reason: total surface area of cylinder= 2πr(r+h)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

36) Assertion: the curved surface area of right circular  cylinder  is 4.4 sq.cm the radius of base is O.7 cm the height of cylinder will be 5 cm

Reason: curved surface area of cylinder 2(πr+h)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: d) both Assertion and reason are false

37) Assertion: the radius of a sphere is 2r then it’s volume will be (32/3)πr^3

Reason: volume of sphere 4/3 πr^3

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

38) Assertion: the radius of hemispherical balloon increase from 6 cm to 12 cm as air is being pumped into it the ratio of the surfaces areas of balloon in two cases is 1:4

Reason: total surface area of hemisphere=3πr^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

39) Assertion: the lateral surface area of a cube is 256 m^2:the volume of the cube is 512m^3

Reason: lateral surface area of cube = 4*side^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

40) Assertion: a cylinder and right circular cone are having the same base and same height the volume of cylinder is three times the volume of cone

Reason: if the radius of cylinder is doubled and height is halved the volume will be doubled

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

41) Assertion: the total surface area of a cone 968 sq.units with radius 14 units and slant height 8 units.

Reason: surface area of cone = πr^2l

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: c)  Assertion is correct but reason is false

42) Assertion: the lateral surface area of a right cone is 62.82 if the radius is 4 cm and the slant height is 5 cm.

Reason: lateral surface area of cone = πrl

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

43) Assertion: 550 cm^3 is the volume of cylindrical shape of water container that has height of 7 cm and diameter of 10 cm

Reason: volume of cylinder= πr^2h

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

44) Assertion: the perpendicular distance between two bases is the height of cylinder

Reason: the line segment joining the centre of two bases is the axis of cylinder

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

45) Assertion: if the value of the side of cube is10 cm then 500vm^2 and  3000 cm^3 its surface area and volume.

Reason: surface area and volume of cube are always equal

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: d) both Assertion and reason are false

46) Assertion: volume of cuboid is defined as the amount of space occupied by the walls of cuboid in three dimensional space

Reason: volume of cuboid is the product of length ,width ,height

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion

47) Assertion: a sphere is a symmetrical object

Reason: a sphere had an only a curved surface no flat surface no edge and no vertices

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

48) Assertion: sphere has constant mean curvature

Reason: sphere has constant width and circumference

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion

49) Assertion: circle ,rectangles ,square and triangles arevplane figure

Reason: plane figure posses perimeter and area

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

50) Assertion: solid figures are three dimensional figures

Reason: solid figures possess volume and surface area.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion

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