# Mathematics Questions and Answers – Surface Area and Volume of Different Solid Shapes

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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

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

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

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

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)

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 cm2
b) 1514.76 cm2
c) 1519.76 cm2
d) 1419.76 cm2

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

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

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

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

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

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