Question

The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Then the ratio of their volumes is
(a) 10 : 17
(b) 20 : 27
(c) 17 : 27
(d) 20 : 37

Answer 1

(b) 20 : 27

Volume of a cylinder = $\mathrm{\pi }{R}^{\mathit{2}}H$, where R = radius and H = height
Suppose that the radii of the cylinders are 2r and 3r and their respective heights are 5h and 3h.
∴ Ratio of volumes = $\frac{\mathrm{\pi }{\left(2\mathrm{r}\right)}^2\times 5\mathrm{h}}{\mathrm{\pi }{\left(3\mathrm{r}\right)}^2\times 3\mathrm{h}}=\frac{20r^{2}h}{27r^{2}h}=\frac{20}{27}$