Question

The surface areas of tWO Spheres are in the ratio 4:9. Find the ratio of their volumes.​

Answer 1

Answer:

The ratio of curved surface area of two spheres is 4 : 9. ∴ The ratio of their volume 8 : 27.

Answer 2

Answer:

the ratio of their volumes is 8/27.

Step-by-step explanation:

Formula of area of sphere is 4πr².

Let, the radius of greater and smaller sphere be R and r respectively.

$\frac{area \: of \: smaller \: sphere}{area \: of \: greater \: sphere} = \frac{4}{9} \\ \frac{4\pi {r}^{2} }{4\pi {R}^{2} } = \frac{4}{9} \\ \frac{ {r}^{2} }{ {R}^{2} } = \frac{4}{9} \\ taking \: square \: root \: both \: side \\ \frac{r}{R} = \frac{2}{3}$

Formula of volume of sphere is 4/3πr³.

$\frac{volume \: of \: smaller \: sphere}{volume \: of \: greater \: sphere} \\ = \frac{ \frac{4}{3}\pi {r}^{3}}{ \frac{4}{3}\pi {R}^{3}} \\ = { (\frac{r}{R})}^{3} \\ = { (\frac{2}{3})}^{3} \\ = \frac{8}{27}$