Question

The curved surface of a cylinder is 1320 cm²,and its base diameter is 21 cm. Find the volume of the cylinder.

Answer 1

Base diameter of cylinder = 21 cm
Then, radius of the base of cylinder = $\frac{21}{2}$ = 10.5 cm
Suppose the height of the cylinder is h cm.
So , curved surface area of cylinder = $2\mathrm{\pi rh}=2\times \frac{22}{7}\times 10.5\times \mathrm{h}$ = $1350{\mathrm{cm}}^2$
$$\begin{gathered} \Rightarrow 44\times 1.5h=1350 \\ \Rightarrow h=\frac{1350}{44\times 1.5}=20.45 \end{gathered}$$
So height of cylinder is 20.45 cm.
So volume of cylinder = ${\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times {\left(10.5\right)}^2\times 20.45=\frac{22}{7}\times 10.5\times 10.5\times 20.45=7085.925{\mathrm{cm}}^3$