Question

Two circular cylinders of equal volume have their heights in the ratio 1 : 3. The ratio of their radii is

• A. $4:\sqrt{3}$
• B. $3:2\sqrt{3}$
• C. $2:\sqrt{3}$
• D. $3:\sqrt{3}$

Answer 1

The correct option is D $3:\sqrt{3}$

Let the height of these two cylinders be $h_1$ and $h_2$, respectively.

Let the height of these two cylinders be $r_1$ and $r_2$, respectively.

Since,

$\frac{h_1}{h_2}=\frac{1}{3}$

We know that the volume of cylinder

$V=\pi r^{2}h$

Since, the volume of these two cylinders

$\pi r_1^2{h}_1=\pi {r_2}^2{h}_2$

$\frac{r_1^2}{r_2^2}=\frac{h_2}{h_1}$

$\frac{r_1^2}{r_2^2}=\frac{3}{1}$

$\frac{r_1}{r_2}=\frac{\sqrt{3}}{1}$

$\frac{r_1}{r_2}=\frac{3}{\sqrt{3}}$

Hence, this is the answer.