Question

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

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

Answer 1

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

Let the height be h and 2h and redii be r and R

$\therefore \pi r^{2}h=\pi R^{2}2h$

$\Rightarrow r^{2}h=R^{2}2h$

$\Rightarrow \frac{r^2}{R^2}=\frac{2h}{h}$

$\Rightarrow \frac{r^2}{R^2}=\frac{2}{1}$

$\Rightarrow \frac{r}{R}=\frac{\sqrt{2}}{1}$

$\Rightarrow r:R=\sqrt{2}:1$