Question

the volume of two hemi-sphere are in the ratio 8:27. find the ratio of their radii.

Answer 1

we know that
volume of hemisphere is 2/3πr³
let the radii of first hemisphere is R
let the radii of second hemisphere is r
then
2/3πR³/2/3πr³=8/27
2/3π will cancel with each other
R³/r³=8/27
R/r=2/3
ratio of there radii is 2/3

Answer 2

Answer:

2:3

Step-by-step explanation:

Volume of hemisphere = $\frac{2}{3} \pi r^{3}$

Let the radius of first hemisphere be r

Let the radius of second hemisphere = R

So, Volume of first sphere =  $\frac{2}{3} \pi r^{3}$

Volume of second sphere =  $\frac{2}{3} \pi R^{3}$

Since we are given that the volume of two hemi-sphere are in the ratio 8:27

So, $\frac{\frac{2}{3} \pi r^{3}}{\frac{2}{3} \pi R^{3}}= \frac{8}{27}$

$\frac{r^{3}}{R^{3}}= \frac{8}{27}$

$\frac{r}{R}= \sqrt[3]{\frac{8}{27}}$

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

Hence the ratio of radii is 2:3