Question

the ratio of surface area of a sphere and curved surface area of a hemisphere is 9:2 find ratio of their volumes

Answer 1

Answer:

Ratio of volumes of Sphere and Hemisphere is 27 : 8

Step-by-step explanation:

Given: Ratio of surface are of Sphere and hemisphere = 9 : 2

To find: Ratio of their volume

$\frac{Surface\:area\:of\:Sphere}{Surface\:area\:of\:Hemisphere}=\frac{4\pi r^2}{2\pi R^2}$

$\frac{9}{2}=\frac{2r^2}{R^2}$

$\frac{9}{4}=\frac{r^2}{R^2}$

$\frac{r}{R}=\sqrt{\frac{9}{4}}$

$\frac{r}{R}=\frac{3}{2}$

$\frac{Volume\:of\:Sphere}{Volume\:of\:Hemisphere}=\frac{\frac{4}{3}\pi r^3}{\frac{2}{3}\pi R^3}$

                                   $=\frac{r^3}{R^3}$

                                   $=(\frac{r}{R})^3$

                                   $=(\frac{3}{2})^3$

                                   $=\frac{27}{8}$

Therefore, Ratio of volumes of Sphere and Hemisphere is 27 : 8