Question

The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is 20:___.

• A. 27

Answer 1

The correct option is A 27
Let $V_1$ be the volume of a cylinder whose radius is 'r' and height is 'h' and

$V_2$ be the volume of a cylinder whose radius is 'R' and height is 'H'.

Given, r : R = 2 : 3 and h : H = 5 : 3.

We know, volume of cylinder $=\pi r^{2}h$,
where 'r' and 'h' are its radius and height.

$\therefore \frac{V_1}{V_2}=\frac{\pi r^{2}h}{\pi R^{2}H}=(\frac{r}{R}{)}^2\times \frac{h}{H}={\left(\frac{2}{3}\right)}^2\times \frac{5}{3}=\frac{20}{27}$