Question

The ratio of the radii of two cylinders is $1:\sqrt{3}$ and their heights are in the ratio $2:3$. The ratio of their volumes is

• A. $1:9$
• B. $2:9$
• C. $4:9$
• D. $5:9$

Answer 1

The correct option is B $2:9$

Volume of a cylinder $=\pi r^{2}h$

Let $r_1$ and $h_1$ be the radius and height of the first cylinder and $r_2$ and $h_2$ be the radius and height of the second cylinder.

Required ratio $=\frac{\pi r_2^1{h}_1}{\pi r_2^2{h}_1}={\left(\frac{r_1}{r_2}\right)}^2\times \frac{h_1}{h_2}$

$={\left(\frac{1}{\sqrt{3}}\right)}^2\times \frac{2}{3}=\frac{2}{9}=2:9$