If the surface areas of two spheres are in the ratio of 4 : 25, then the ratio of their volumes is:

The surface area of a sphere is, A = $$4\pi r^2$$

Let the radii of the two spheres be a and b. Given that their surface areas are in the ratio:

A1:A2= $$\dfrac{4}{25}$$

Substituting the formula for surface area:

$$4\pi a^2$$:$$4\pi b^2$$ = 4:25

Canceling 4π from both sides:

$$a^2:b^2=4:25$$

Taking the square root on both sides:

a:b = 2:5

Now, the volume of a sphere is V = $$\dfrac{4}{3}\pi r^3$$

The ratio of their volumes is:

V1:V2= $$a^3:b^3$$ = 8:125