Question

Two equal volumes circular cylinders have their heights in the ratio $2:1.$ The ratio of their radii is

• A. $2:1$
• B. $1:2$
• C. $\sqrt{2}:1$
• D. $1:\sqrt{2}$

Answer 1

The correct option is D $1:\sqrt{2}$

We know volume of cylinder $=\pi r^{2}h$

Given, $\pi r_1^2{1}_1=\pi r_2^2{1}_2$
Also given, $\frac{1_1}{1_2}=\frac{2}{1}$

$\Rightarrow {\left(\frac{r_1}{r_2}\right)}^2=\frac{1_2}{1_1}=\frac{1}{2}$
$\Rightarrow \frac{r_1}{r_2}=\frac{1}{\sqrt{2}}$
So, ratio of radii of two cylinders $=$ $1:\sqrt{2}$