This set of Mathematics Quiz for Schools focuses on “Surface Area and Volume of Different Solid Shapes”.

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

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 m^{2}

b) 659.4 m^{2}

c) 650.4 m^{2}

d) 689.4 m^{2}

View Answer

Explanation: Total surface area of a cylinder = 2πr(h + r)

= 2 × \(\frac {22}{7}\) × 7 × (8 + 7)

= 659.4 m

^{2}

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 cm^{2}

b) 1052 cm^{2}

c) 1153.4 cm^{2}

d) 3172 cm^{2}

View Answer

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 cm

^{2}

4. What is the formula for the volume of a right circular cone?

a) \(\frac {1}{3}\)πr^{3}h

b) \(\frac {1}{3}\)πr^{2}h

c) \(\frac {1}{2}\)πr^{2}h

d) \(\frac {1}{2}\)πr^{3}h

View Answer

Explanation: Volume of right circular cone = \(\frac {1}{3}\)πr

^{2}h

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) 2πr^{2}h

b) 2πrh

c) 2π(r + h)

d) 2π(rh)

View Answer

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.

6. What is the total surface area of an iron sphere having a radius of 11 cm?

a) 1529.76 cm^{2}

b) 1514.76 cm^{2}

c) 1519.76 cm^{2}

d) 1419.76 cm^{2}

View Answer

Explanation: The total surface area of an iron sphere = 4πr

^{2}

= 4 × \(\frac {22}{7}\) × 11

^{2}

= 1519.76 cm

^{2}

7. What is the volume of a hemisphere if the radius of the hemisphere is 3 m?

a) 135.4 m^{3}

b) 56.52 m^{3}

c) 120.23 m^{3}

d) 105.5 m^{3}

View Answer

Explanation: Radius of the hemisphere = \(\frac {2}{3}\)πr

^{3}

= \(\frac {2}{3}\) × 3.14 × 3

^{3}

= 56.52 m

^{3}

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

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 cm^{2} 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

Explanation: The lateral surface area of a right circular cone is 2020 cm

^{2}.

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 m^{2} and a height of 23 m.

a) 4793 m^{3}

b) 2763 m^{3}

c) 2783 m^{3}

d) 4783 m^{3}

View Answer

Explanation: The volume of the right prism = Area of base × height

= 121 × 23

= 2783 m

^{3}

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 m^{2}

b) 2263 m^{2}

c) 2200 m^{2}

d) 4783 m^{2}

View Answer

Explanation: The lateral surface area of a cuboid = 2h(l + b)

= 2 × 22 (27 + 23)

= 2200 m

^{2}

12. Find the total surface area of a square-shaped box having a length of 2 m for its side.

a) 47 m^{2}

b) 22 m^{2}

c) 24 m^{2}

d) 48 m^{2}

View Answer

Explanation: The total surface area of a cube = 6a

^{2}

= 6 × 2

^{2}

= 24 m

^{2}

**Sanfoundry Global Education & Learning Series – Mathematics – Class 10**.

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