Question

The radius and height of a cylinder are in the ratio 7 : 2. If the volume of the cylinder is 8316 cm³, find the total surface area of the cylinder.

Answer 1

We have: $\frac{radius}{height}=\frac{7}{2}$
i.e., $r=\frac{7}{2}h$
Now, volume $={\mathrm{\pi r}}^2\mathrm{h}=\mathrm{\pi }{\left(\frac{7}{2}\mathrm{h}\right)}^2\mathrm{h}=8316{\mathrm{cm}}^3$
$$\begin{gathered} \Rightarrow \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times h^3=8316 \\ \Rightarrow h^3=\frac{8316\times 2}{11\times 7}=108\times 2=216 \\ \Rightarrow h=\sqrt[3]{216}=6cm \end{gathered}$$

Then $r=\frac{7}{2}h=\frac{7}{2}\times 6=21cm$
∴ Total surface area $=2\mathrm{\pi r}(h+r)=2\times \frac{22}{7}\times 21\times (6+21)=3564{\mathrm{cm}}^2$