OUR OWN HIGH SCHOOL, DUBAI

PRACTICE WORKSHEET

SURFACE AREA AND VOLUME

1 MARK

1 Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

2 A right circular cylinder of radius r cm and height h cm (ℎ > 2𝑟) just encloses a sphere of diameter

(a) rcm (b) 2r cm (c) h cm (d) 2h cm

3 If two solid hemispheres of same base radius r are joined together along their bases, then curved
surface area of this new solid is
(a) 4𝜋𝑟2 (b) 6𝜋𝑟2 (c) 3𝜋𝑟2 (d) 8𝜋𝑟2

4 A cylinder, a cone and a hemisphere are of the same base and same height. The ratio of their
volumes is
(a) 1 : 2: 3 (b) 3 : 1 : 2 (c)2 : 1 : 3 (d)3 : 2: 1

5 If the radius and height of a cylinder are in the ratio 5 : 7 and its volume is 550 cm 3, then its radius
is equal to
(a)6 cm (b)7 cm (c)5 cm (d)10 cm.

6 The length of the longest pole that can be put in a room of dimensions (10 m × 10 m × 5m) is
(a) 15 m (b) 16 m (c) 10 m (d) 12 m
7 If a cylinder is covered by two hemispheres shaped lid of equal shape, then the total curved surface
area of the new object will be
(a) 4πrh + 2πr2 (b) 4πrh – 2πr2 (c) 2πrh + 4πr2 (d) 2πrh + 4πr
8 In a cylinder, radius is doubled and height is halved, curved surface area will be
(a) halved (b) doubled (c) same (d) four times
9 Two identical solid cubes of side a are joined end to end. Then the total surface area of the
resulting cuboid is
(a) 12a2 (b) 10a2 (c) 8a2 (d) 11a2

10 If the volume and surface area of a sphere are numerically equal, then the radius of the sphere is

(a)4 units (b)1 unit (c)2 units (d)3 units

11 If the curved surface area of a solid right circular cylinder of a height h and radius r is one third of
its total surface area, then
1 1
(a)ℎ = 3 𝑟 (b) ℎ = 2 𝑟 (c) h=r (d)h= 2r
12 If the radius and slant height of a cone are in the ratio 4 : 7 and its curved surface area is 792 cm2,
then its radius is
(a)10 cm (b)8 cm (c)12 cm (d)9 cm
13 If the volume of a vessel in the form of a right circular cylinder is 448𝜋cm3 and its height is 7 cm,
then the curved surface area of the cylinder is
(a)224 𝜋cm2 (b)212 𝜋cm2 (c)112 𝜋cm2 (d)none of these
3
14 If the volume of a cube is given as 1331 cm , the length of its edge is equal to
(a) 11 cm (b) 12 cm (c)13 cm (d)14 cm
15 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) 4.2 (b) 2.1 (c) 8.1 (d) 1.05
16 Assertion: If the volume of two sphere are in the ratio 27: 8 then their surface areas are in the
ratio 9:4
4
Reason: Volume of sphere=3 𝜋𝑟 3 and it’s surface area 4 𝜋𝑟 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 correct explanation for assertion
c) assertion is correct but reason is false
d) both assertion and reason are false

17 Assertion: If the radius of a cone is halved and volume is not changed, then height remains same.
Reason: If the radius of a cone is halved and volume is not changed then height must become four
times of the original 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 correct explanation for assertion
c) assertion is correct but reason is false
d)assertion is wrong and reason is correct.

18 Assertion: Total Surface area of the top is the sum of the curved surface area of the hemisphere
and the curved surface area of the cone.
Reason: Top is obtained by fixing the plane surfaces of the hemisphere and cone together.

a) both assertion and reason are correct and reason is correct explanation for assertion
b) both assertion and reason are correct but reason is correct explanation for assertion
c) assertion is correct but reason is false
d)assertion is wrong and reason is correct.
19 Assertion: Two identical solid cubes of side a are joined end to end. Then the total surface area of
the resulting cuboid is 10a2
Reason: The total surface area of a cube having side a = 6a2

a) both assertion and reason are correct and reason is correct explanation for assertion
b) both assertion and reason are correct but reason is correct explanation for assertion
c) assertion is correct but reason is false
d)assertion is wrong and reason is correct.

20 Assertion: A solid is in the form of a cone standing on a hemisphere with both their radii being
equal to 1 cm and the height of the cone is equal to its radius, then the volume of the solid is
𝜋 cm3.
1 2
Reason: Volume of the cone is =3 𝜋𝑟 2 ℎ and volume of the hemi-sphere is 3 𝜋𝑟 3 .
a)Both Assertion and Reason are correct and reason is correct explanation for the.
b) Both Assertion and Reason are false but reason is not correct explanation for assertion.
c) Assertion is correct but reason is false.
d) Both Assertion and reason are false.
2 MARKS

21 If the TSA of a solid hemisphere is 462 sq.cm, find its volume.(Take π=22/7)

22 A solid ball is exactly fitted inside the cubical box of side a. Find the volume of the ball.

23 The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of
radius 4 cm. Find the height of the cone. (Take π=22/7).
24 From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find
the volume of the remaining solid.

25 The radius of a sphere is increased by 10%. Prove that the volume will be increased by 33.1%
approximately.

3 MARKS

26 A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the
cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right
circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the
toy. (Take 𝜋 = 3.14)
27 1 22
The volume of a hemisphere is 2425 𝑐𝑚3 . Find its curved surface area. [𝜋 = ]
2 7

28 The sum of the radius of base and height of a solid right circular cylinder is 37cm.If the total surface
area of the solid cylinder is 1628sq.cm, find the volume of the cylinder.
29 A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 7 cm
22
and the height of the cone is equal to its diameter. Find the volume of the solid. [𝜋 = ]
7

30 A rectangular water tank of base 11 m x 6 m contains water up to a height of 5 m. If the water in

the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the
tank.

5 MARKS

31 Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm
× 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the
volume of this liquid. Give your answer to the nearest integer. [Use π=3.14 ]

32 Lead spheres of diameter 6cm are dropped into a cylindrical beaker containing some water and
are fully submerged. If the diameter of the beaker is 18cm and water rises by 40cm. find the no. of
lead sphere dropped in the water.

33 A sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to
the volume of the cube is √6 : √𝜋.

34

35 A golf ball has diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate total
surface area which is exposed to the surroundings assuming that the dimples are hemispherical.
36

Answers:

1. (d) 16 : 9 8. (c) same 15. (b) 2.1 22. πa3/6 29. 821.2 cm³

2. (b) 2r cm 9. (b) 10a2 16. c) 23. 3cm 30. 8.6 m

3. (a) 4𝜋𝑟2 10. (d)3 units 17. d) 24. 277 cm3 31. 488.16 cm³

1
4. (b) 3 : 1 : 2 11. (b) ℎ = 𝑟 18. a) 25. proof 32. 90
2

5. (c)5 cm 12. (c)12 cm 19. a) 26. 25.12 cm3 33. proof

6. (a) 15 m 13. (c)112 𝜋cm2 20. a) 27.693cm2 34.

7. (c) 2πrh + 4πr2 14. (a)11 cm 21. 718.67cm3 28. 4620 cm3 35.71.68cm2

36. 273cm2
Answer 33.

34 Answer:
35 Answer:

36 Answer: