Question

The total surface area of a cylinder is 462 cm². Its curved surface area is one-third of its total surface area. Find the volume of the cylinder.

Answer 1

Total surface area = 462 cm²

Given: Curved surface area =$\frac{1}{3}$$\times$total surface area = $\frac{1}{3}\times 462=154{\mathrm{cm}}^2$

Now, total surface area − curved surface area = $2\mathrm{\pi rh}+2{\mathrm{\pi r}}^2-2\mathrm{\pi rh}$
$$\begin{gathered} \Rightarrow \Rightarrow 462-154=2\mathrm{\pi }{r}^2 \\ \Rightarrow 308=2\times \frac{22}{7}\times r^2 \\ \Rightarrow r^{\mathit{2}}=\frac{308\times 7}{44}=49 \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$

Now, curved surface area = 154 cm²

$$\begin{gathered} \Rightarrow 2\mathrm{\pi }rh=154 \\ \Rightarrow 2\times \frac{22}{7}\times 7\times h=154 \\ \Rightarrow h=\frac{154}{44}=3.5\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\mathrm{\pi }{r}^{\mathit{2}}h\mathit{} \\ =\frac{22}{7}\times 7^2\times 3.5 \\ =539{\mathrm{cm}}^3 \end{gathered}$$