Question

The radius and height of a cylinder are in the ratio 5 : 7 and its volume is 550 cm³. Find its radius and height.

Answer 1

$$\begin{gathered} \frac{\mathrm{Radius}}{\mathrm{height}}=\frac{r}{h}=\frac{5}{7} \\ \Rightarrow r=\frac{5}{7}h \end{gathered}$$
Now, volume$={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times \frac{5}{7}\mathrm{h}\times \frac{5}{7}\mathrm{h}\times \mathrm{h}=550c{m}^3$
$$\begin{gathered} \therefore h=\sqrt[3]{\frac{550\times 7\times 7\times 7}{22\times 5\times 5}}=7cm \\ \mathrm{Also},r=\frac{5}{7}h=5cm \end{gathered}$$