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.)

Answer 1

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.

$$\begin{gathered} \therefore 2\mathrm{\pi }rh=94.2{\mathrm{cm}}^2 \\ \Rightarrow 2\times 3.14\times r\times 5=94.2 \\ \Rightarrow r=\frac{94.2}{2\times 3.14\times 5}=3\mathrm{cm} \end{gathered}$$
Thus, the radius of the cylinder is 3 cm.

(ii) Volume of the cylinder = $\mathrm{\pi }{r}^{2}h=3.14\times {\left(3\right)}^2\times 5$ = 141.3 cm³

Thus, the volume of the cylinder is 141.3 cm³.