Welcome to the Surface Areas and Volumes Mock Test for Class 9 Mathematics, created in accordance with the latest NCERT and CBSE curriculum.
This test is designed to help students revise, practice, and apply the concepts from one of the most important and practical chapters in Geometry — Surface Areas and Volumes.

Through this test, students can explore how mathematical formulas connect with the real world, understand the relationship between 2D and 3D shapes, and strengthen their problem-solving abilities for school exams, Olympiads, and competitive assessments.

1. Ratio of the volume of a cone and a cylinder of same radius of base and same height is

1 : 1

1 : 2

1 : 3

1 : 4

2. If volume of a cube is 216 cm³, then its edge is

36cm

6cm

12cm

16cm

3. Three cubes are joined end to end forming a cuboid. If side of a cube is 3 cm, then dimensions of the cuboid are :

l = 2, b = 2, h = 2

l = 4, b = 4, h = 2

l = 4, b = 2, h = 4

l = 9, b = 3, h = 3

4. In a Gym, in one exercise you have to continuously toss solid cylindrical jumbles and catch them.

Cylindrical jumbles are of length 1 m and base diameter also 1 m. Density of the wood used is 4 kg per m3, then the weight tossed is

3.14 kg

4π kg

12.56 kg

5. Slant height of a cone is 34 cm and base diameter is 32 cm, then height of the cone is

33 cm

25 cm

30 cm

27 cm

6. How do we judge that the given object is a solid object ?

by touching it.

by finding its dimensions.

distance between any two points of the object remains same.

by keeping it on the table and noting down whether the whole object touches the table or not.

7. If the radius (r) of a sphere is reduced to its half then, new volume would be:

(a)

(b)

(c)

(d)

8. A basket ball is just packed in a cube of side 20 cm, then the surface area of the basket ball is

120 cm2

2400 cm2

400π cm2

1256 cm2

9. Number of surfaces of the same area in a cube are

10. A cylindrical jar is full of water upto the brim, a sphere of radius 0.35 cm is immersed in the water, how much water will flow out of the jar?

0.18 cm2

0.18 cm3

1.54 cm2

1.54 cm3

11. The diameter of a sphere is decreased by 25%, by what percentage its volume decreases?

25%

57.81%

53.50%

50%

12. For Diwali celebrations, a packet of “Conical Diwas” is bought. In that, there are 15 conical diwas, with red glittering polish surface. Jaya took a scale and noted the following informations :

Radius of the base is 7 cm and slant height is 10 cm. Then calculate how much total area is polished.

5160 cm2

5601 cm2

6501 cm2

5610 cm2

13. Diameter of the earth is four times (approximately) the diameter of the moon, then the ratio of their surface areas is

4 : 1

8 : 1

16 : 1

2 : 1

14. Lateral surface area of a cuboid with dimensions l, b, h is

2(lb + bh + lh) – 2lb

2(lb + bh + lh)

2(l + b) h2

lbh

15. Given a cuboid of dimensions l = 6 cm, b = 5 cm, h = 4 cm. How many cubes, each of side 2 cm can be cut out from it?

none of these

16. Two cubes of side 3 cm each are joined end to end, then the volume of the cuboid so formed is

32 cm3

16 cm3

54 cm3

8 cm3

17. In a split A.C., the inner cooler is formed by a cooling pipe to the outer instrument. The length of the pipe is 3 m and diameter is cm. When A.C. is switched on, then the surface of the pipe cooled in the process has area

3π m2

0.015 π m2

150π cm2

300π cm2

18. A conical tent is to accommodate 11 persons. Each person requires 4 square metres of the space on the ground and 20 cubic metres of air to breath, then the height of the cone is

10cm

12cm

`15cm

18cm

19. A cylindrical cake of maximum volume is to be cut out of a cube cake of side 4 cm. Then the maximum volume of the cake is

16 π cm2

32 π cm2

20. Given a cuboid of dimensions l = 3 cm, b = 2 cm, h = 2 cm. How many cubes of 1 cm side can be cut out of it ?

21. A student has rectangular sheet of dimensions 14 cm × 22 cm. He wants to make a cylinder in such a way so that volume is minimum, then its height should be

14 cm

22 cm

14 cm or 22 cm

none of these

22. If volume and surface area of a sphere is numerically equal, then its radius is

2units

3units

4units

5units

23. A gift pack is in cuboidal shape of dimensions 1.5 m, 0.75 m, 0.5 m. Tanya didn’t like the paper wrapped on the gift pack, so she removed it and wrapped the gift pack with a paper of her choice but left the base, which she says will fill with her name. The difference of area of wrapping papers used is (ignore the extra paper used to mould the corners.)

1.125 cm2

0.375 cm2

0.75 m2

2.75 m2

24. Number of surfaces of the same area in a cuboid are

25. The total surface area of a cone whose radius is and slant height is 2l is

(a)

(b)

(c)

(d)

26. Charvi has a rectangular sheet of paper and wants to fold it in such a manner that the cylinder thus formed should have maximum surface area. Then she should fold it,

along length

along breadth

along any of the sides length or breadth

27. A belan is in the form of a cylinder of length 14 cm and diameter 4 cm. It is used to make a chapati (Roti). How much roti, it will flat while rolling once ?

188.57 cm2

182.28 cm2

176.00 cm2

170.50 cm2

28. The dimensions of a cuboid are 3 cm, 2 cm, 1 cm. Then the length of diagonal of the cuboid is

(a)

(b)

(c)

(d)

29. A metallic sheet is of the rectangular shape with dimensions 48 cm × 36 cm. From each of its corners, a square of 8 cm is cut off and an open box is made of the remaining sheet, then

the volume of the box is

5120 cm2

5012 cm3

5012 cm2

5120 cm3

30. A cylinder of base radius ‘r’ and height ‘h’ is dipped vertically to half the height, in a bucket full of purple paint. Then the area of the surface which gets painted is

(a)

(b)

(c)

(d)

31. If surface area of a sphere is 676 π cm², then its radius is equal to

12 cm

13 cm

9 cm

8 cm

Question 1 of 31