Two cylinders of the same volume have their radii in the ratio 2 1. the ratio of their heights is

Distribute the referral code to your friends and ask them to register with Tutorix using this referral code.

Once we get 15 subscriptions with your referral code, we will activate your 1 year subscription absolutely free.

Your subscribed friend will also get 1 month subscription absolutely free.

>

Question 52 Two cylinders of same volume have their radii in the ratio 1: 6. Then, ratio of their heights is

Solution

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

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

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

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

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

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

$\therefore h_1:h_2=36:1$