Question

The radii of two cylinder are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes and the ratio of their curved surfaces.

Answer 1

Suppose that the radii of the cylinders are 2r and 3r and the respective heights are 5h and 3h.
Now, ratio of their volumes = $\frac{\mathrm{volume}\mathrm{of}\mathrm{first}\mathrm{cylinder}}{\mathrm{volume}\mathrm{of}\mathrm{second}\mathrm{cylinder}}=\frac{\mathrm{\pi }\mathit{(}\mathit{2}r{\mathit{)}}^{\mathit{2}}\mathit{\times }\mathit{5}h}{\mathrm{\pi }{\left(\mathit{3}r\right)}^{\mathit{2}}\mathit{\times }\mathit{3}h}=\frac{4\times 5}{9\times 3}=\frac{20}{27}=20:27$

Also, ratio of their curved surface areas = $\frac{\mathit{2}\pi \mathit{\times }\mathit{2}r\mathit{\times }\mathit{5}h}{\mathit{2}\pi \mathit{\times }\mathit{3}r\mathit{\times }\mathit{3}h}=\frac{10}{9}=10:9$