CBSE Class 10 Mathematics Surface Area and Volume Assignment Set B

1. A metallic solid cone is melted to form a solid cylinder of equal radius. If the height of the cylinder is 6 cm, then the height of the cone was

(a) 10 cm 

(b) 12 cm

(c) 18 cm 

(d) 24 cm

Answer : (C)

2. If four times the sum of the areas of two circular faces of a cylinder of height 8 cm is equal to twice the curved surface area, then diameter of the cylinder is

(A) 4 cm 

(B) 8 cm

(C) 2 cm 

(D) 6 cm

Answer : (B)

3. 12 spheres of the same size are made from melting a solid cylinder of diameter 16 cm and 2 cm height. The diameter of each sphere is

(A) 3cm 

(B) 2 cm

(C) 3 cm 

(D) 4 cm

Answer : (B)

4. The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

(A) 4/3π

(B) 10/3π

(C) 5π 

(D) 20/3 *5π

Answer : (A)

5. The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is

(A) 3 cm 

(B) 4 cm

(C) 6 cm 

(D) 12 cm

Answer : (D)

6. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is

(A) 12π cm3 

(B) 3 15π cm

(C) 3 16π cm 

(D) 3 20π cm

Answer : (C)

7. A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h. If the total volume of the solid is 3times the volume of the cone, then the height of the circular cylinder is

(A) 2h 

(B) 2h /3

(C) 3h/2

(D) 4h

Answer : (B)

8. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, then the height above the base at which the section has been made is

(A) 10 cm 

(B) 15 cm

(C) 20 cm 

(D) 25 cm

Answer : (C)

9. The number of solid spheres, each of diameter 6 cm that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm is

(A) 3 

(B) 4

(C) 5 

(D) 6

Answer : (C)

10. 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) 4:9

Answer : (D)

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

(A) 490 m 

(B) 525 m

(C) 665 m 

(D) 860 m

Answer : (B)

12. 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 cm²

Answer : (D)

13. 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) 5:1

Answer : (D)

14. In a shower, 5 cm of a 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 m³

Answer : (C)

15. The sum of length, breadth and height of cuboid is 19 cm and its diagonal is 5 5cm . Its surface area is

(A) 361 cm² 

(B) 125 cm²

(C) 236 cm² 

(D) 486 cm²

Answer : (C)

16. The volume of a wall which is 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 cm

Answer : (B)

17. A mason constructs a wall of dimension (270 cm ×300 cm ×350 cm) with bricks, each of size (22.5 cm ×11.25 cm ×8.75 cm) and it is assumed that 1/8 space is covered by the cement. Number of bricks used to construct the wall is

(A) 11000 

(B) 11100

(C) 11200 

(D) 11300

Answer : (C)

18. The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 m². The dimensions are

(A) 2m, 4m, 6m 

(B)1 m, 2 m, 3 m 

(C) 4 m, 5 m, 6 m 

(D) 6m, 8m, 10 m

Answer : (A)

19. The curved surface area of one cone is twice that of the other cone. The slant height of the second is twice that of the first one, then ratio of their radii is

(A) 4 : 1 

(B) 3 : 1 

(C) 2 : 1 

(D) 5 : 1

Answer : (A)

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

(A) 20% 

(B) 40% 

(C) 60% 

(D) 72.8%

Answer : (D)

21. 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 : 3

Answer : (B)

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

(A) xyz 

(B) 2xyz 

(C) xyz 

(D) 3xyz

Answer : (C)

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

(A)29 m 

(B) 21 m 

(C)19 m 

(D)17 m

Answer : (D)

24. Volumes of two solid spheres are in the ratio 125 : 64. Determine their radii, if the sum of their radii is 45 cm.

(A) 25cm, 20cm 

(B)15cm, 30cm 

(C)35cm, 10cm 

(D)40cm, 5cm

Answer : (A)

25. A semi-circular thin sheet of paper of diameter 28 cm is bent and an open conical cup is made.Find the capacity of the cone.

(A)311.2 cm³ 

(B) 622.36 cm³ 

(C)30.51 cm³ 

(D)152 m³

Answer : (B)

26. The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube is

(A) π : 8 

(B) π : 6 

(C) 8 : π 

(D) 6 : π

Answer : (D)

27. If a cone is cut into two parts by a horizontal plane passing trough the mid-points of its axis, the ratio of the volumes of the upper part and the cone is

(A) 1 : 2 

(B) 1 : 4

(C) 1 : 6 

(D) 1 : 8

Answer : (D)

28. A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. Then the height of the cone is

(A) 3x cm 

(B) x cm

(C) 4x cm 

(D) 2x cm

Answer : (C)

29. If the radii of the circular ends of frustum of a cone are 20 cm and 12 cm and its height is 6 cm, then the slant height of frustum (in cm) is

(A) 10 

(B) 8

(C) 12 

(D) 15

Answer : (A)

30. The volume of a sphere (in cu. cm) is numerically equal to its surface area (in sq. cm). The diameter of the sphere (in cm) is

(A) 3 

(B) 6

(C) 2 

(D) 4

Answer : (B)

31. The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is

(A) 9.7 cm³ 

(B) 77.6 cm³

(C) 58.2 cm³ 

(D) 19.4 cm³

Answer : (D)