Class 10 Maths Chapter 13 Surface Areas and Volumes MCQ

This set of Class 10 Maths Chapter 13 Multiple Choice Questions & Answers (MCQs) focuses on “Surface Areas and Volumes”. These MCQs are created based on the latest CBSE syllabus and the NCERT curriculum, offering valuable assistance for exam preparation.

1. A funnel is in the shape of a right circular cone with a base radius of 3 cm and a height of 4 cm. Find the slant height of the funnel.
a) 4 cm
b) 5 cm
c) 7 cm
d) 7.5 cm
View Answer

Answer: b
Explanation: Slant height = \(\sqrt {h^2+r^2}\)
= \(\sqrt {4^2+3^2}\)
= \(\sqrt {16+9}\)
= √25
= 5 cm

2. What is the total surface area of a cylinder with a radius of 7 m and a height of 8 m?
a) 609.4 m²
b) 659.4 m²
c) 650.4 m²
d) 689.4 m²
View Answer

Answer: b
Explanation: Total surface area of a cylinder = 2πr(h + r)
= 2 × \(\frac {22}{7}\) × 7 × (8 + 7)
= 659.4 m²

3. A right circular cone has a radius of 7 cm and a height of 24 cm. Find the area of the sheet required to make 7 such cones.
a) 3846.5 cm²
b) 1052 cm²
c) 1153.4 cm²
d) 3172 cm²
View Answer

Answer: a
Explanation: Slant height = \(\sqrt {h^2+r^2}\)
= \(\sqrt {24^2+7^2}\)
= \(\sqrt {576+49}\)
= 25 cm
Area required to make 7 such cones = 7 × Lateral surface area of a right circular cone
= 7 × (πrl)
= 7 × 3.14 × 7 × 25
= 3846.5 cm²

4. What is the formula for the volume of a right circular cone?
a) \(\frac {1}{3}\)πr³h
b) \(\frac {1}{3}\)πr²h
c) \(\frac {1}{2}\)πr²h
d) \(\frac {1}{2}\)πr³h
View Answer

Answer: b
Explanation: Volume of right circular cone = \(\frac {1}{3}\)πr²h
Where ‘r’ is the radius of the base and ‘h’ is the height of the right circular cone.

5. What is the formula for the curved surface area of a rectangular circular cylinder?
a) 2πr²h
b) 2πrh
c) 2π(r + h)
d) 2π(rh)
View Answer

Answer: b
Explanation: The curved surface area of a rectangular circular cylinder = 2πrh
Where ‘r’ is the radius of the base and ‘h’ is the height of the right circular cylinder.

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6. What is the total surface area of an iron sphere having a radius of 11 cm?
a) 1529.76 cm²
b) 1514.76 cm²
c) 1519.76 cm²
d) 1419.76 cm²
View Answer

Answer: c
Explanation: The total surface area of an iron sphere = 4πr²
= 4 × \(\frac {22}{7}\) × 11²
= 1519.76 cm²

7. What is the volume of a hemisphere if the radius of the hemisphere is 3 m?
a) 135.4 m³
b) 56.52 m³
c) 120.23 m³
d) 105.5 m³
View Answer

Answer: b
Explanation: Radius of the hemisphere = \(\frac {2}{3}\)πr³
= \(\frac {2}{3}\) × 3.14 × 3³
= 56.52 m³

8. Find the slant height of the right circular cone if the base diameter of the right circular cone is 14 cm and the height is 24 cm.
a) 11 cm
b) 13 cm
c) 28 cm
d) 25 cm
View Answer

Answer: d
Explanation: Radius (r) = \(\frac {diameter}{2} = \frac {14}{2}\) = 7 cm
Slant height = \(\sqrt {h^2+r^2}\)
= \(\sqrt {24^2+7^2}\)
= \(\sqrt {576+49}\)
= 25 cm

9. The lateral surface area of a right circular cone is 2020 cm² and its radius is 10 cm. What is its slant height?
a) 28.3 cm
b) 25.6 cm
c) 68.23 cm
d) 64.33 cm
View Answer

Answer: d
Explanation: The lateral surface area of a right circular cone is 2020 cm².
πrl = 2020
3.14 × 10 × l = 2020
l = \(\frac {2020}{3.14 \times 10}\)
= 64.33 cm

10. Find the volume of the right prism with an area of base 121 m² and a height of 23 m.
a) 4793 m³
b) 2763 m³
c) 2783 m³
d) 4783 m³
View Answer

Answer: c
Explanation: The volume of the right prism = Area of base × height
= 121 × 23
= 2783 m³

11. Find the lateral surface area of a rectangular room with a height of 22 m, length 27 m and a breadth of 23 m.
a) 4793 m²
b) 2263 m²
c) 2200 m²
d) 4783 m²
View Answer

Answer: c
Explanation: The lateral surface area of a cuboid = 2h(l + b)
= 2 × 22 (27 + 23)
= 2200 m²

12. Find the total surface area of a square-shaped box having a length of 2 m for its side.
a) 47 m²
b) 22 m²
c) 24 m²
d) 48 m²
View Answer

Answer: c
Explanation: The total surface area of a cube = 6a²
= 6 × 2²
= 24 m²

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