Question

IF THE RATIO OF RADII OF TWO SPHERES IS 2:3 ,FIND THE RATIO OF THEIR VOLUMES.

Answer 1

8:27 is answer for this

Answer 2

ANSWER WITH FULL EXPLANATION

If the radius of a sphere is $r$, then the volume of the sphere is calculated by this formula: $V=\frac{4}{3}\pi r^{3}$. 

Solution for this question
Let $r_{1}$ and $r_{2}$ be the radii of the two spheres. 
Let $V_{1}$ and $V_{2}$ be the volumes of the two spheres respectively. 

Now, 
Volume of the sphere with $r_{1}$ as its radius = $\frac{4}{3} \pi r_{1}^{3}$
Volume of the sphere with $r_{2}$ as its radius = $\frac{4}{3} \pi r_{2}^{3}$

It is clearly given in the question, that the ratio of radii of the two spheres is $2:3$. So, we can also write it as 
$r_{1}:r_{2}=2:3$
⇒ $\frac{r_{1}}{r_{2}} = \frac{2}{3}$                                       ...(1)

Now, 
$\frac{V_{1}}{V_{2}}$
$= \frac{\frac{4}{3} \pi r_{1}^{3}}{\frac{4}{3} \pi r_{2}^{3}}$
$= \frac{r_{1}^{3}}{r_{2}^{3}}$
$= (\frac{r_{1}}{r_{2}})^{3}$
$= (\frac{2}{3})^{3}$                                          [ Using (1) ]
$= \frac{2^{3}}{3^{3}}$
$= \frac{8}{27}$
$=8:27$

∴ The ratio of volumes of the two spheres is $8:27$. 

Hope this may help you. 

If you have any doubt, then you can ask me in the comments.