Question

The ratio of the curved surface area and the total surface area of a circular cylinder is 1 : 2 and the total surface area is 616 cm². Find its volume.

Answer 1

Total surface area of cylinder = 616 cm²
The ratio of the curved surface area and the total surface area of cylinder is 1 : 2.
∴ 2(Curved surface area) = total surface area

$$\begin{gathered} 2\left(2\mathrm{\pi }rh\right)=2\mathrm{\pi }rh+2\mathrm{\pi }{r}^2 \\ \Rightarrow 2\mathrm{\pi }rh=2\mathrm{\pi }{r}^2 \\ \Rightarrow rh\mathit{}=r^{\mathit{2}} \\ \Rightarrow r\mathit{}\mathit{=}h \\ \mathrm{Also},\mathrm{we}\mathrm{have}: \\ 2\mathrm{\pi }rh+2\mathrm{\pi }{r}^2=616 \\ \Rightarrow 4\mathrm{\pi }{r}^2=616 \\ \Rightarrow r^2=\frac{616\times 7}{88}=49 \\ \Rightarrow r=7\mathrm{cm} \\ \mathrm{i}.\mathrm{e}.,h=7\mathrm{cm} \\ \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{cylinde}r=\mathrm{\pi }{r}^{\mathit{2}}h \\ =\frac{22}{7}\times 7\times 7\times 7 \\ =1078{\mathrm{cm}}^3 \end{gathered}$$