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:

• A. 4:9
• B. 9:4
• C. 20:27
• D. 27:20

Answer 1

The correct option is C 20:27

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.

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