Question

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is
(a) 27 : 20
(b) 20 : 27
(c) 4 : 9
(d) 9 : 4

Answer 1

(b) 20 : 27

Suppose that the radii of the cylinders are 2r and 3r and their respective heights are 5h and 3h..
$$\begin{gathered} \therefore \mathrm{Ratio}\mathrm{of}\mathrm{their}\mathrm{volumes}=\frac{\mathrm{\pi }{\left(2r\right)}^2\times 5h}{\mathrm{\pi }{\left(3r\right)}^2\times 3h} \\ =\frac{4\times 5}{9\times 3}=\frac{20}{27} \end{gathered}$$