Question

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

• A. $1:2$
• B. $1:4$
• C. $2:1$
• D. $\sqrt{2}:1$

Answer 1

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

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

Let height, radius and volume of first cylinder be $h_1,r_1,v_1$ and of second cylinder be $h_2,r_2,v_2$

$\frac{v_1}{v_2}=\frac{{\pi r_1^{2}h}_1}{{\pi r_2^{2}h}_2}$

$\frac{h_1}{h_2}=\frac{1}{2};\frac{v_1}{v_2}=1;\frac{r_1}{r_2}=?$

$\frac{v_1}{v_2}=\frac{r_1^2}{r_2^2}.\frac{1}{2}\Rightarrow 1={\left(\frac{r_1}{r_2}\right)}^2=\times 2\Rightarrow {\left(\frac{r_1}{r_2}\right)}^2=2\Rightarrow \frac{r_1}{r_2}=\sqrt{2}$

$\therefore r_1:r_2=\sqrt{2}:1$