CBSE Class 10 Mathematics Surface Areas and Volumes MCQs Set D

Question. A cone of radius 20 cm is divided into two parts by drawing a plane through the midpoint of its axis parallel to the base. The ratio of the volumes of the two parts is
(a) 1 : 4
(b) 1 : 2
(c) 1 : 7
(d) 1 : 3

Answer: C

Question. A rectangular piece of paper is 44 cm long and 18 cm wide. If a cylinder is formed by rolling the paper along its length, then the radius of the base of the cylinder is
(a) 14 cm
(b) 21 cm
(c) 7 cm
(d) 22 cm

Answer: C

Question. A hollow sphere of external and internal diameters 8cm and 4cm respectively is melted into a cone of base diameter 8cm. The height of the cone is
(a) 14cm
(b) 13cm
(c) 12cm
(d) 15cm

Answer: A

Question. The maximum volume of a cone that can be carved out of a solid hemisphere of radius ‘r’ is
(a) πr³
(b) 2/3 πr³
(c) 1/3 πr³
(d) 1/3 πr²h

Answer: C

Question. The edge of the cube whose volume is 1728 cu.cm is
(a) 72cm
(b) 18cm
(c) 17cm
(d) 12cm

Answer: D

Question. The height of a cone whose base area and volume are equal numerically is
(a) 9 units
(b) 3 units
(c) 6 units
(d) 1 unit

Answer: B

Question. If the radii of two spheres are in the ratio 2 : 3, then the ratio of their respective volumes is
(a) 8 : 27
(b) 3 : 5
(c) 7 : 24
(d) 5 : 14

Answer: A

Question. The edge of a cube whose volume is 8x3 is
(a) x
(b) 2x
(c) 4x
(d) 8x

Answer: B

Question. In a right circular cone, the cross-section made by a plane parallel to the base is a
(a) Triangle
(b) Circle
(c) Square
(d) None of the options

Answer: B

Question. 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

Answer: A

Question. A frustum of a cone is of height 12cm with radii of its circular ends as 2cm and 4cm. The volume of the frustum is
(a) 352cm³
(b) 350cm³
(c) 354cm³
(d) None of the options

Answer: A

Question. Test tube available in a chemistry lab is a combination of
(a) a hemisphere and a cylinder
(b) a hemisphere and a cone
(c) a cone and a cylinder
(d) None of the options

Answer: A

Question. The surface area of a cube whose volume is 64 is
(a) 96 sq. cm
(b) 72 sq. cm
(c) 64 sq. cm
(d) 108 sq. cm

Answer: A

Question. The perpendicular distance between the two parallel circular bases is called the ______ of the frustum of the cone.
(a) radius
(b) height
(c) slant height
(d) volume

Answer: B

Question. The radius of a sphere (in cm) whose volume is 12p cm³, is
(a) 3
(b) 3√3
(c) 32/3
(d) 31/3

Answer: C

Question. If the surface area of a sphere is 144p, then its radius is
(a) 6 cm
(b) 8 cm
(c) 12 cm
(d) 10 cm

Answer: A

Question. If two solid hemispheres of same base radius ‘x’ cm are joined together along their bases, then the CSA of the new solid formed is
(a) 4π x² cm²
(b) 5π x² cm²
(c) 8π x² cm²
(d) 6π x² cm²

Answer: A

Question. A cone is cut through a plane parallel to its base and the small cone is (upper part) remove(d) The part that is left over is called
(a) cylinder
(b) cone
(c) sphere
(d) frustum of a cone

Answer: D

Question. The inner dimensions of a closed box are 12cm, 10cm and 8cm. If the thickness of the wood is 1cm, then the capacity of the box is
(a) 1200 cu.cm
(b) 1920 cu.cm
(c) 480 cu.cm
(d) 960 cu.cm

Answer: D

Question. Frustum is a _______ word
(a) Greek
(b) English
(c) Latin
(d) None of the options

Answer: A

Question. 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

Answer: A

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) 3πr²
(c) 2πr²
(d) πr²

Answer: A

Question. The volume of the cuboid whose length, breadth and height is 12cm, 8cm and 6cm is
(a) 568 cu.cm
(b) 576 cu.cm
(c) 570 cu.cm
(d) 576 sq.cm

Answer: B

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

Answer: A

Question. If the volume of a 7 cm high right circular cylinder is 448p cm³, then its radius is equal to
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm

Answer: D

Question. The edge of a cube whose volume is equal to that of a cuboid of dimensions 8 cm × 4 cm × 2 cm is
(a) 6 cm
(b) 4 cm
(c) 2 cm
(d) 8 cm

Answer: B

Question. The longest rod that can be placed inside the cube is
(a) 3 edge
(b) √2 edge
(c) √3 edge
(d) √5 edge

Answer: C

Question. The shape of a glass tumbler is usually in the form of
(a) a cylinder
(b) a sphere
(c) a cone
(d) frustum of a cone

Answer: D

Question. If three metallic spheres of radii 6cm, 8cm and 10cm are melted to form a single sphere, the diameter of the sphere is
(a) 26cm
(b) 30cm
(c) 24cm
(d) 36cm

Answer: C

Question. Three cubes of metal whose edges are 3cm, 4cm and 5cm are melted and a single cube is formed.  The edge of the single cube so formed is
(a) 4cm
(b) 8cm
(c) 5cm
(d) 6cm

Answer: D

Question. In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(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.

Question. Assertion (A): Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm².     
Reason (R): If r be the radius and h be the height of the cylinder, then total surface area = (2πrh + 2πr²).

Answer: A

Question. Assertion (A): 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 (R): If r is the radius and h the height of the cone, then slant height = √h² + r² 

Answer: D

Question. Assertion (A): The number of coins 1.75 cm in diameter and 2 mm thick is formed from a melted cuboid 10 cm × 5.5 cm × 3.5 cm is 400.     
Reason (R): Volume of a cylinder = πr²h cubic units and volume of cuboid = (l × b × h) cubic units.

Answer: A

One Word Questions

Question. What is the total surface area of a solid hemisphere of radius R?
Answer: 3πR²

Question. If surface area of sphere is 144 cm². What is its radius?
Answer: 6cm

Question. Volume of right circular cylinder is 448 cm³, height of cylinder is 7cm; Find the radius.
Answer: 8cm

Question. A well of diameter 2m is dug 14m deep. Find the volume of the earth dug out.
Answer: 44m³

Question. In a shower, there is 5cm rain falls. Find in cubic metre the volume of water that falls on 2 hectares of ground. (1 hectare = 10,000 m²)
Answer: 1000m³

Question. What is the length of the largest rod that can be put in a box of inner dimensions 30cm, 24cm and 18cm?
Answer: 30 √2cm

Question. The total surface area of the cube is 216cm². Find its edge.
Answer: 6cm

Question. What will be the volume of a cylindrical tank with radius 7cm and height 2cm.?
Answer: 308cm³

Question. Cube of sides 2cm is cut down into cubes of sides 1cm. What is the ratio of surface area of smalller cubes to that of larger cube?
Answer: 1 : 4

Question. If lateral surface area of a cube is 64cm² , what will be its edge?
Answer: 4cm

Question. Find the radius of the largest right circular cone that can be cut out of a cube whose edge is 9cm.
Answer: 4.5cm

Question. Find the edge of cube if volume of the cube is equal to the volume of cuboid of dimensions 8×4× 2.
Answer: 4cm

Question. A right circular cylinder is closed at both ends, whose flat area is equal to its total curve surface. What is the relationship between r and h?
Answer: r = h

Question. If height of frustum is 4cm and the radii of two bases are 3cm and 6cm respectively, find the slant height of the frustum.
Answer: 5cm

Question. Two cubes each of length 5m edge are joined end to end. What will be the surface area of the resulting cuboid?
Answer: 250m²

Question. What is the number of solid spheres of radius 1/2 cm , which may be formed from a solid sphere of radius 2cm?
Answer: 64

Question. A wooden box of dimensions 8m×7m×6m is to carry rectangluar boxes of dimension 8cm×7cm×6cm,find the maximum number of boxes that can be carried out in the wooden box.
Answer: 10,00,000

Question. Curved surface area of a cone is 90 cm². What will be the radius of the cone if its slant height is 90cm?
Answer: 1cm

Question. Radius of sphere is 8cm. How many small spheres of radii 4cm can be formed out of it?
Answer: 8

Question. Find the area of cardboard needed to make a rectangular box 14cm long, 9cm wide and 7cm high.
Answer: 574m²

Question. The area of rhombus is 24cm² and one of its diagonal is 8cm. What is other diagonal of the rhombus?
Answer: 6cm

Question. If the semi-vertical angle of a cone of height 3cm is 600 , find its volume.
Answer: 27 cm³

Question. Volume of hemisphere is 18 cm³, what will be its radius?
Answer: 3cm

Question. If the volume and surface area of a sphere are numerically same, then what is its radius?
Answer: 3

Question. Volume of a cuboid is 240cm³ . If its lenght is 4cm, breadth is 5cm, find the height of the cuboid.
Answer: 12cm