Question

Two cylinders of the same volume have their radii in the ratio $1:6.$ Then, the ratio of their heights is

Answer 1

Let $r_1$, $r_2$ be the radii and $h_1$, $h_2$ be the heights of two cylinders.

Given, $\frac{r_1}{r_2}=\frac{1}{6}$

Now, according to the question, we have

$\pi r_1^2{h}_1=\pi r_2^2{h}_2$ [$\because$ volume of cylinder $=\pi r^{2}h$]

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

$\Rightarrow {\left(\frac{r_1}{r_2}\right)}^2=\frac{h_2}{h_1}$

$\Rightarrow {\left(\frac{1}{6}\right)}^2=\frac{h_2}{h_1}$

$\Rightarrow \frac{1}{36}=\frac{h_2}{h_1}$

$\Rightarrow \frac{h_1}{h_2}=\frac{36}{1}$

$\therefore h_1:h_2=36:1$