Question

The volume of a solid cylinder is 1584 cm³ and its height is 14 cm. Find its total surface area.

Answer 1

Let r cm be the radius of the base of the cylinder.
Volume of the solid cylinder = 1584 cm³
Height of the solid cylinder, h = 14 cm
We have:

$$\begin{gathered} \frac{22}{7}\times r^2\times 14=1584 \\ \Rightarrow r^2=\frac{1584}{44}=36 \\ \Rightarrow r=6\mathrm{cm} \end{gathered}$$


$$\begin{gathered} \therefore \mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cylinder}=2\mathrm{\pi }r(r\mathit{}\mathit{+}\mathit{}h\mathit{}) \\ =2\times \frac{22}{7}\times 6\times (6+14) \\ =\frac{44\times 6\times 20}{7} \\ =754.29{\mathrm{cm}}^2 \end{gathered}$$