Question

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 cm³, then find the radius of the base of the cylinder.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{base}\mathrm{and}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cylinder}\mathrm{be}r\mathrm{and}h,\mathrm{respectively}. \\ \mathrm{We}\mathrm{have}, \\ r:h=2:3\mathrm{i}.\mathrm{e}.\frac{r}{h}=\frac{2}{3} \\ \mathrm{or}h=\frac{3r}{2}.....\left(\mathrm{i}\right) \\ \mathrm{As}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=12936{\mathrm{cm}}^3 \\ \Rightarrow \mathrm{\pi }{r}^{2}h=12936 \\ \Rightarrow \frac{22}{7}\times r^2\times \frac{3r}{2}=12936\left[\mathrm{Using}\left(\mathrm{i}\right)\right] \\ \Rightarrow \frac{33}{7}\times r^3=12936 \\ \Rightarrow r^3=12936\times \frac{7}{33} \\ \Rightarrow r^3=2744 \\ \Rightarrow r=\sqrt[3]{2744} \\ \therefore r=14\mathrm{cm} \end{gathered}$$

So, the radius of the base of the cylinder is 14 cm.