Please refer to Surface Area and Volume MCQ Questions Class 10 Mathematics below. These MCQ questions for Class 10 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Surface Area and Volume will help you to prepare for the exams and get more marks.

**Surface Area and Volume MCQ Questions Class 10 Mathematics**

Please see solved MCQ Questions for Surface Area and Volume in Class 10 Mathematics. All questions and answers have been prepared by expert faculty of standard 10 based on the latest examination guidelines.

**MCQ Questions Class 10 Mathematics Surface Area and Volume**

**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 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) 352cm^{3}

(b) None of these

(c) 354cm^{3}

(d) 350cm^{3}

**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) None of these

(d) a cone and a cylinder

**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 x^{2} cm^{2}

(b) 5π x^{2} cm^{2}

(c) 8π x^{2} cm^{2}

(d) 6π x^{2} cm^{2}

**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 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. 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) πr^{3}

(b) 2/3 πr^{3}

(c) 1/3 πr^{3}

(d) 1/3 πr^{2}h

**Answer**

C

**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. 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 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. 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. 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. 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) None of these

(c) Latin

(d) English

**Answer**

A

**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 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 8x ^{3} is **

(a) x

(b) 2x

(c) 4x

(d) 8x

**Answer**

B

**Question. If the volume of a 7 cm high right circular cylinder is 448p cm ^{3}, then its radius is equal to **

(a) 2 cm

(b) 4 cm

(c) 6 cm

(d) 8 cm

**Answer**

D

**Question. The radius of a sphere (in cm) whose volume is 12p cm3, is **

(a) 3

(b) 3√3

(c) 3^{2/3}

(d) 3^{1/3}

**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. 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

**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 cm ^{2}. **

**Reason (R): If r be the radius and h be the height of the cylinder, then total surface area = (2πrh + 2πr**

^{2}).**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 = √h ^{2} + r^{2} .**

**Answer**

D

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

(a) 4cm

(b) 8cm

(c) 5cm

(d) 6cm

**Answer**

D

**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 these

**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 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) 4πr^{2}

(b) 3πr^{2}

(c) 2πr^{2}

(d) πr^{2}

**Answer**

A

**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): 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 = πr ^{2}h 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. What will be the volume of a cylindrical tank with radius 7cm and height 2cm.?**

**Answer**

308cm^{3}

**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. 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. If the semi-vertical angle of a cone of height 3cm is 600 , find its volume.**

**Answer**

27 cm³

**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. If lateral surface area of a cube is 64cm ^{2} , 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. Volume of hemisphere is 18 cm³, what will be its radius?**

**Answer**

3cm

**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. 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 240cm ^{3} . If its lenght is 4cm, breadth is 5cm, find the height of the cuboid.**

**Answer**

12cm

**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. A well of diameter 2m is dug 14m deep. Find the volume of the earth dug out.**

**Answer**

44m^{3}

**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 m ^{2})**

**Answer**

1000m³

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

**Answer**

574m^{2}

**Question. The area of rhombus is 24cm ^{2} and one of its diagonal is 8cm. What is other diagonal of the rhombus?**

**Answer**

6cm

**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**

250m^{2}

**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