NCERT Exemplar Problems – Class 10 Mathematics
Chapter 12: Surface Areas and Volumes
Multiple Choice Questions (Exercise 12.1) with Correct Answers
Source: NCERT Exemplar Problems Class 10 Mathematics (Official Answer Key)
1. A cylindrical pencil sharpened at one edge is the combination of
(A) a cone and a cylinder (B) frustum of a cone and a cylinder (C) a hemisphere and a cylinder (D) two cylinders
Correct Answer: (A)
2. A surahi is the combination of
(A) a sphere and a cylinder (B) a hemisphere and a cylinder (C) two hemispheres (D) a cylinder and a cone
Correct Answer: (A)
3. A plumbline (sahul) is the combination of (see Fig. 12.2)
(A) a cone and a cylinder (B) a hemisphere and a cone (C) frustum of a cone and a cylinder (D) sphere and cylinder
Note: Refer to Fig. 12.2 in the original book.
Correct Answer: (B)
4. The shape of a glass (tumbler) (see Fig. 12.3) is usually in the form of
(A) a cone (B) frustum of a cone (C) a cylinder (D) a sphere
Note: Refer to Fig. 12.3 in the original book.
Correct Answer: (B)
5. The shape of a gilli, in the gilli-danda game (see Fig. 12.4), is a combination of
(A) two cylinders (B) a cone and a cylinder (C) two cones and a cylinder (D) two cylinders and a cone
Note: Refer to Fig. 12.4 in the original book.
Correct Answer: (C)
6. A shuttle cock used for playing badminton has the shape of the combination of
(A) a cylinder and a sphere (B) a cylinder and a hemisphere (C) a sphere and a cone (D) frustum of a cone and a hemisphere
Correct Answer: (D)
7. A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called
(A) a frustum of a cone (B) cone (C) cylinder (D) sphere
Correct Answer: (A)
8. A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that \(\dfrac{1}{8}\) space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is
(A) 142296 (B) 142396 (C) 142496 (D) 142596
Correct Answer: (A)
9. A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8 cm. The height of the cone is
(A) 12 cm (B) 14 cm (C) 15 cm (D) 18 cm
Correct Answer: (B)
10. A solid piece of iron in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm, is moulded to form a solid sphere. The radius of the sphere is
(A) 21 cm (B) 23 cm (C) 25 cm (D) 19 cm
Correct Answer: (A)
11. A mason constructs a wall of dimensions 270 cm × 300 cm × 350 cm with the bricks each of size 22.5 cm × 11.25 cm × 8.75 cm and it is assumed that \(\dfrac{1}{8}\) space is covered by the mortar. Then the number of bricks used to construct the wall is
(A) 11100 (B) 11200 (C) 11000 (D) 11300
Correct Answer: (B)
12. Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
(A) 4 cm (B) 3 cm (C) 2 cm (D) 6 cm
Correct Answer: (C)
13. The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is
(A) 4950 cm² (B) 4951 cm² (C) 4952 cm² (D) 4953 cm²
Correct Answer: (A)
14. A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is
(A) 0.36 cm³ (B) 0.35 cm³ (C) 0.34 cm³ (D) 0.33 cm³
Correct Answer: (A)
15. 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) \(4\pi r^{2}\) (B) \(6\pi r^{2}\) (C) \(3\pi r^{2}\) (D) \(8\pi r^{2}\)
Correct Answer: (A)
16. A right circular cylinder of radius \(r\) cm and height \(h\) cm (\(h > 2r\)) just encloses a sphere of diameter
(A) \(r\) cm (B) \(2r\) cm (C) \(h\) cm (D) \(2h\) cm
Correct Answer: (B)
17. During conversion of a solid from one shape to another, the volume of the new shape will
(A) increase (B) decrease (C) remain unaltered (D) be doubled
Correct Answer: (C)
18. The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is
(A) 32.7 litres (B) 33.7 litres (C) 34.7 litres (D) 31.7 litres
Correct Answer: (A)
19. In a right circular cone, the cross-section made by a plane parallel to the base is a
(A) circle (B) frustum of a cone (C) sphere (D) hemisphere
Correct Answer: (A)
20. 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
Correct Answer: (D)
Answers taken from the official NCERT Exemplar answer key.