Question

If the surface areas of two spheres are in the ratio 4:9, then the ratio of their radis is​

Answer 1

Answer:

8:27

Step-by-step explanation:

Let r and R are two radius of a spheres.

According to the question,

$⇒\frac{ 4πr {}^{2} }{ 4πR {}^{2} } = \frac{4}{9}$

$⇒ \frac{r {}^{2} }{ R {}^{2} } = \frac{4}{6}$

Taking square root on both sides.

$⇒ \frac{r}{ R } = \frac{2}{3} ---- ( 1 )$

The volume of two spheres are in ratio

$⇒ \frac{ \frac{4}{3} \pi \: r {}^{3} } { \frac{4}{3}\pi \: R {}^{3} }$

$⇒ \frac{r {}^{3} }{ R {}^{3} }$

From ( 1 ),

$⇒ \frac{(2) {}^{3} }{(3) {}^{3} }$

$⇒ \frac{8}{27}$

Therefore, the required ratio is 8:27