Class 10 Maths MCQs for Chapter 13 Surface Areas and Volumes with Answers PDF

MCQs for Class 10 Maths Chapter 13 Surface Areas and Volumes are available here with solved answers. These questions are made according to the latest CBSE syllabus and NCERT textbook. Practising them can help students understand the chapter better and score well in the board exam. Students can also download a free PDF for extra practice and revision.

MCQs for Class 10 Maths Chapter 13 Surface Areas and Volumes

Question 1: The curved surface area of a cone depends on:

Options:

(A). Radius only

(B). Slant height only

(C). Radius and slant height

(D). Height only

Correct Answer: (C). Radius and slant height

Explanation: The formula for the curved surface area of a cone is πrl. So, both radius and slant height are required.

Question 2: What is the volume of a cube whose side is 5 cm?

Options:

(A). 25 cm³

(B). 75 cm³

(C). 100 cm³

(D). 125 cm³

Correct Answer: (D). 125 cm³

Explanation: Volume of a cube = a³

= 5³ = 125 cm³

Question 3: The total surface area of a sphere is four times its:

Options:

(A). Radius

(B). Diameter

(C). Base area

(D). Great circle area

Correct Answer: (D). Great circle area

Explanation: The total surface area of a sphere is 4πr², while the area of its great circle is πr².

Question 4: The shape formed by rotating a right triangle about one of its perpendicular sides is:

Options:

(A). Sphere

(B). Cylinder

(C). Cone

(D). Cuboid

Correct Answer: (C). Cone

Explanation: When a right triangle rotates around one of its perpendicular sides, a cone is formed.

Question 5: Find the total surface area of a cube having side 4 cm.

Options:

(A). 16 cm²

(B). 64 cm²

(C). 96 cm²

(D). 128 cm²

Correct Answer: (C). 96 cm²

Explanation: Total surface area of cube = 6a²

= 6 × 4²

= 6 × 16 = 96 cm²

Question 6: The volume of a cylinder is obtained by multiplying:

Options:

(A). Base area and height

(B). Radius and height

(C). Diameter and height

(D). Circumference and height

Correct Answer: (A). Base area and height

Explanation: Volume of cylinder = Base area × Height

= πr²h

Question 7: A hemisphere has:

Options:

(A). One flat surface and one curved surface

(B). Two curved surfaces

(C). Only one flat surface

(D). Only curved surface

Correct Answer: (A). One flat surface and one curved surface

Explanation: A hemisphere has one circular flat surface and one curved outer surface.

Question 8: Which solid has exactly one curved surface?

Options:

(A). Cube

(B). Sphere

(C). Cuboid

(D). Prism

Correct Answer: (B). Sphere

Explanation: A sphere contains only one continuous curved surface.

Question 9: The total surface area of a cuboid includes:

Options:

(A). Only top and bottom faces

(B). Only side faces

(C). Area of all six faces

(D). Curved surface only

Correct Answer: (C). Area of all six faces

Explanation: The total surface area is the sum of the areas of all six rectangular faces.

Question 10: What is the radius of a sphere whose diameter is 18 cm?

Options:

(A). 6 cm

(B). 9 cm

(C). 18 cm

(D). 36 cm

Correct Answer: (B). 9 cm

Explanation: Radius = Diameter ÷ 2

= 18 ÷ 2 = 9 cm

Question 11: The curved surface area of a cylinder with radius 7 cm and height 10 cm is:

Options:

(A). 70π cm²

(B). 140π cm²

(C). 210π cm²

(D). 490π cm²

Correct Answer: (B). 140π cm²

Explanation: Curved surface area = 2πrh

= 2 × π × 7 × 10

= 140π cm²

Question 12: Which formula is used to find the curved surface area of a hemisphere?

Options:

(A). πr²

(B). 2πr²

(C). 3πr²

(D). 4πr²

Correct Answer: (B). 2πr²

Explanation: The curved part of a hemisphere has area equal to 2πr².

Question 13: The slant height of a cone is always:

Options:

(A). Smaller than radius

(B). Equal to height

(C). Greater than height

(D). Zero

Correct Answer: (C). Greater than height

Explanation: Slant height is found using √(r² + h²), so it is always greater than the height.

Question 14: The volume of a sphere mainly depends on:

Options:

(A). Radius

(B). Diameter only

(C). Height

(D). Slant height

Correct Answer: (A). Radius

Explanation: The formula for the volume of a sphere is 4/3 πr³.

Question 15: Find the volume of a cube whose edge is 3 cm.

Options:

(A). 9 cm³

(B). 18 cm³

(C). 27 cm³

(D). 36 cm³

Correct Answer: (C). 27 cm³

Explanation: Volume of cube = a³

= 3³ = 27 cm³

Question 16: The curved surface area of a cone is measured in:

Options:

(A). cm

(B). cm²

(C). cm³

(D). litre

Correct Answer: (B). cm²

Explanation: Surface area always measures the outer covering of a solid, so it is expressed in square units.

Question 17: If the radius of a sphere is doubled, its volume becomes:

Options:

(A). Double

(B). Four times

(C). Six times

(D). Eight times

Correct Answer: (D). Eight times

Explanation: Volume of a sphere depends on r³.

When radius becomes 2r:

(2r)³ = 8r³

So, the volume becomes 8 times.

Question 18: A cuboid has length 5 cm, breadth 4 cm and height 3 cm. Its volume is:

Options:

(A). 12 cm³

(B). 20 cm³

(C). 60 cm³

(D). 120 cm³

Correct Answer: (C). 60 cm³

Explanation: Volume of cuboid = l × b × h

= 5 × 4 × 3

= 60 cm³

Question 19: The base of a cylinder is:

Options:

(A). Square

(B). Triangle

(C). Circle

(D). Rectangle

Correct Answer: (C). Circle

Explanation: A cylinder has two circular bases connected by a curved surface.

Question 20: What is the total surface area of a sphere of radius 5 cm?

Options:

(A). 25π cm²

(B). 50π cm²

(C). 100π cm²

(D). 125π cm²

Correct Answer: (C). 100π cm²

Explanation: Total surface area of sphere = 4πr²

= 4 × π × 5²

= 4 × π × 25

= 100π cm²

Question 21: The formula 2πr(r + h) is used for finding:

Options:

(A). Volume of cylinder

(B). Curved surface area of cylinder

(C). Total surface area of cylinder

(D). Area of circle

Correct Answer: (C). Total surface area of cylinder

Explanation: This formula includes both circular bases and the curved surface area.

Question 22: Which of the following solids has no edge?

Options:

(A). Cube

(B). Cone

(C). Cylinder

(D). Sphere

Correct Answer: (D). Sphere

Explanation: A sphere has only one curved surface and no edges or vertices.

Question 23: The capacity of a water tank is related to its:

Options:

(A). Surface area

(B). Volume

(C). Perimeter

(D). Radius

Correct Answer: (B). Volume

Explanation: Capacity tells us how much a container can hold, which depends on volume.

Question 24: The volume of a cone with radius 3 cm and height 4 cm is:

Options:

(A). 12π cm³

(B). 24π cm³

(C). 36π cm³

(D). 48π cm³

Correct Answer: (A). 12π cm³

Explanation: Volume of cone = 1/3 πr²h

= 1/3 × π × 3² × 4

= 1/3 × π × 9 × 4

= 12π cm³

Question 25: Which solid has both flat and curved surfaces?

Options:

(A). Sphere

(B). Cone

(C). Cube

(D). Cuboid

Correct Answer: (B). Cone

Explanation: A cone contains one flat circular base and one curved surface.

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