CBSE Class 10 Mathematics Surface Areas and Volumes MCQs Set E

Question. If the radius of the sphere is increased by 100%, the volume of the corresponding sphere is increased by
(a) 200%
(b) 500%
(c) 700%
(d) 800%

Answer: C

Question. A sphere is melted and half of the melted liquid is used to form 11 identical cubes, whereas the remaining half is used to form 7 identical smaller spheres. The ratio of the side of the cube to the radius of the new small sphere is
(a) (4/3)^1/3
(b) (8/3)^1/3
(c) (3)^1/3
(d) 2

Answer: B

Question. The base radii of a cone and a cylinder are equal. If their curved surface areas are also equal, then the ratio of the slant height of the cone to the height of the cylinder is
(a) 2 : 1
(b) 1 : 2
(c) 1 : 3
(d) 3 : 1

Answer: A

Question. If the perimeter of one face of a cube is 20 cm, then its surface area is
(a) 120 cm²
(b) 150 cm²
(c) 125 cm²
(d) 400 cm²

Answer: B

Question. Ratio of lateral surface areas of two cylinders with equal height is
(a) 1 : 2
(b) H :h
(c) R : r
(d) None of these

Answer: C

Question. Ratio of volumes of two cylinders with equal height is
(a) H :h
(b) R : r
(c) R² : r²
(d) None of these

Answer: C

Question. Ratio of volumes of two cones with same radii is
(a) h₁ :h₂
(b) s₁ : s₂
(c) r₁ : r₂
(d) None of these

Answer: A

Question. The diameter of hollow cone is equal to the diameter of a spherical ball. If the ball is placed at the base of the cone, what portion of the ball will be outside the cone?
(a) 50%
(b) less than 50%
(c) more then 50%
(d) 100%

Answer: C

Question. Volume of a spherical shell is given by
(a) 4π (R² − r²)
(b) π (R³ − r³
(c) 4π (R³ − r³)
(d) 4/3 π(R³ −

Answer: D

Question. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is
(a) 12 m
(b) 18 m
(c) 36 m
(d) 66 m

Answer: C

Question. A 20 m deep well, with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. The height of the platform is
(a) 2.5 m
(b) 3.5 m
(c) 3 m
(d) 2 m

Answer: A

Question. From a solid circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed, then the volume of remaining solid is
(a) 280 πcm³
(b) 330 πcm³
(c) 240 πcm³
(d) 440 πcm³

Answer: C

Question. 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

Answer: A

Question. A right circular cylinder of radius r and height h (where, h > 2r ) just encloses a sphere of diameter
(a) r
(b) 2r
(c) h
(d) 2h

Answer: B

Question. 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

Answer: C

Question. A solid piece of iron in the form of a cuboid of dimensions 49 cm x 33 cm x 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

Answer: A

Question. 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

Answer: C

Question. 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

Answer: A

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

Answer: D

Question. Assertion : Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm². 
Reason : If r be the radius and h be the height of the cylinder, then total surface area = (2πrh + 2πr²).
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Answer: A

Question. 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. Then the height of the frustum is 3 cm.
Reason : Slant height of the frustum of the cone is given by l = √(R − r)²+ h² .
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Answer: A

Question. Assertion : If the height of a cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.
Reason : If r be the radius and h be the slant height of the cone, then slant height = √h² + r^{2 .}
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Answer: D

Fill in the blank Questions

Question. The volume of a hemisphere is .......... the volume of a cylinder if its height and radius is same as that of the cylinder.
Answer: two-third

Question. If a solid of one shape is converted to another, then the volume of the new solid..........
Answer: remains same

Question. A sharpened pencil is a combination of .......... and .......... shapes.
Answer: cylinder, cone

Question. If we cut a cone by a plane parallel to its base, we obtain a .......... and ..........
Answer: cone, frustum of a cone

Question. If the radius of a sphere is halved, its volume becomes .......... time the volume of original sphere.
Answer: one-eighth

Question. Surahi is the combination of .......... and ..........
Answer: sphere, cylinder

Question. The volume of a solid is the measurement of the portion of the .......... occupied by it.
Answer: Space

Question. In a right circular cone, the cross-section made by a plane parallel to the base is a ..........
Answer: Circle

Question. Total curved surface area of the frustum is ..........
Answer: π(rn + r²)l + r²₁ + πr²₂

Question. The TSA, CSA stand for .......... and .......... respectively.
Answer: Total surface area, Curved surface area.

Question. A shuttle cock used for playing badminton has the shape of the combination of .......... of cone and hemisphere.
Answer: Frustum

Question. .......... is measured in square units.
Answer: Area

Question. In the gilli-danda game, the shape of a gilli is a combination of two cones and ..........
Answer: Cylinder

Question. .......... is measured in cubic units.
Answer: Volume

Question. A cube is a special type of ..........
Answer: Cuboid