Question

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

Answer 1

Suppose that the curved surface area and the total surface area of the right circular cylinder are x cm² and 2x cm².
Then we have:
2x = 616
x = 308 sq cm
Hence, the curved surface area of the cylinder is 308 sq cm.
Let r cm and h cm be the radius and height of the cylinder, respectively.
$$\begin{gathered} \mathrm{Then}2\mathrm{\pi }rh+2\mathrm{\pi }{r}^2=616{\mathrm{cm}}^2\mathrm{and}2\mathrm{\pi }rh=308{\mathrm{cm}}^2 \\ \therefore 2\mathrm{\pi }rh+2\mathrm{\pi }{r}^2-2\mathrm{\pi }rh=616-308 \\ \Rightarrow 2\mathrm{\pi }{r}^2=308 \\ \Rightarrow 2\times \frac{22}{7}\times r^2=308 \\ \Rightarrow r^2=\frac{308\times 7}{44}=49 \\ \Rightarrow r=7\mathrm{cm} \\ \mathrm{Now},2\mathrm{\pi }rh=308{\mathrm{cm}}^2 \\ \Rightarrow 2\times \frac{22}{7}\times 7\times h\mathit{}=308 \\ \Rightarrow h\mathit{}=\frac{308}{44}=7\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\mathrm{\pi }{r}^{\mathit{2}}h\mathrm{cubic}\mathrm{cm} \\ =\frac{22}{7}\times 7^2\times 7 \\ =1078{\mathrm{cm}}^3 \end{gathered}$$