Two cylinders of equal volume have heights in the ratio 2:3 the ratio of their radii 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.

Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is .

Solution

3 : 1
Let $r_{1}$ , $r_{2}$ be the radii and $h_{1}$ , $h_{2}$ be the heights of two cylinders.
Given, $\frac{h_{1}}{h_{2}} = \frac{1}{9}$ Now, according to the question.,
$π r_{1}^{2} h_{1} = π r_{2}^{2} h_{2}$ $[∴ v o l u m e o f c y l i n d e r = π r^{2} h]$

$\Rightarrow \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{h_{2}}{h_{1}} \Rightarrow {(\frac{r_{1}}{r_{2}})}^{2} = \frac{9}{1} \Rightarrow \frac{r_{1}}{r_{2}} = \frac{\sqrt{9}}{1} \Rightarrow \frac{r_{1}}{r_{2}} = \frac{3}{1}$
Hence, $r_{1} : r_{2} = 3 : 1$

Mathematics

NCERT Exemplar
Standard VIII

Suggest Corrections