Question

Two cylinders of equal volume have their heights in the ratio $2:1$. What is the ratio of their radii?

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

Answer 1

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

Let $V_1$ and $V_2$ be the volumes of two cylinders, then

$V_1=V_2\Rightarrow \pi r_1^2{h}_1=\pi r_2^2{h}_2\Rightarrow \frac{h_1}{h_2}={\left(\frac{r_2}{r_1}\right)}^2$

$\Rightarrow \frac{r_2}{r_1}=\sqrt{\frac{h_1}{h_2}}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$ or $1:$ $\sqrt{2}$