Question

voleum of 2 spheres are in the ratio 27:64 then the ratio of their surface area is ___​

Answer 1

Step-by-step explanation:

Given:

• Ratio of 2 spheres

To Find:

• The ratio of surface area

Solution:

Let the radii of two spheres be r1 and r3

$\tt \leadsto \: \frac{ \frac{4}{3}\pi {r}^{3} _{1} }{\frac{4}{3}\pi {r}^{3}_{2}} = \frac{27}{64} \\ \tt \leadsto \frac{ \cancel{\frac {4}{3}_{1}\pi} {r}^{3} _{1} }{ \cancel{\frac{4}{3}\pi} {r}^{3}_{1}} = \frac{27}{64} \\ \tt \leadsto \: \frac{ {r}^{3} _{1}}{ {r}^{3} _{2}} = \frac{27}{64} \\ \tt \leadsto \: \frac{r_{1}}{r_{2}} = \sqrt[3]{ \frac{27}{64} } = \frac{3}{4}$

Now, to find the ratio of it's surface area=4πr²

So,

$\tt \leadsto \: \frac{r_{1}}{r_{2}} = \frac{3}{4} \\ \tt \leadsto \: \frac{4\pi {r}^{2} _{1}}{4\pi {r}^{2}_{1} } = {( \frac{3}{4} )}^{2} \\ \tt \leadsto \frac{4\pi {r}^{2} _{1}}{4\pi {r}^{2}_{2} } = \frac{9}{16}$

Required ratio=9:16