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.