Question

The radius of the base and the height of a cylinder are in the ratio 2 : 3. If its volume is 1617 cm³, find the total surface area of the cylinder.

Answer 1

Suppose that the radius of the base and the height of the cylinder are 2x cm and 3x cm, respectively.
$$\begin{gathered} \mathrm{Then}1617={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times (2\mathrm{x}{)}^2\times 3\mathrm{x} \\ =\frac{22}{7}\times 12{\mathrm{x}}^3 \\ \Rightarrow {\mathrm{x}}^3=\frac{1617\times 7}{22\times 12}=42.875 \\ \Rightarrow \mathrm{x}=\sqrt[3]{42.875}=3.5\mathrm{cm} \end{gathered}$$

Hence, radius = 7 cm; height of the cylinder = 10.5 cm

$$\begin{gathered} \therefore \mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cylinder}=2\mathrm{\pi }rh+2\mathrm{\pi }{r}^{\mathit{2}} \\ =2\times \frac{22}{7}(7\times 10.5+7\times 7){\mathrm{cm}}^2 \\ =\frac{44}{7}\times (73.5+49){\mathrm{cm}}^2=770{\mathrm{cm}}^2 \end{gathered}$$