# The lateral surface area of a cylinder is 94.2 cm2 and its height is 5 cm. Find

Question:

The lateral surface area of a cylinder is 94.2 cm2 and its height is 5 cm. Find

(i) the radius of its base and

(ii) its volume. (Take π = 3.14.)

Solution:

Height of the cylinder, h = 5 cm

Lateral (or curved) surface area of cylinder = 94.2 cm2

(i) Let the radius of the cylinder be r cm.

$\therefore 2 \pi r h=94.2 \mathrm{~cm}^{2}$

$\Rightarrow 2 \times 3.14 \times r \times 5=94.2$

$\Rightarrow r=\frac{94.2}{2 \times 3.14 \times 5}=3 \mathrm{~cm}$

Thus, the radius of the cylinder is 3 cm.

(ii) Volume of the cylinder $=\pi r^{2} h=3.14 \times(3)^{2} \times 5=141.3 \mathrm{~cm}^{3}$

Thus, the volume of the cylinder is 141.3 cm3.