The surface area of two spheres are in a ratio of 1: 16. what is the ratio of their volume?

Let the radius of the 1st sphere be denoted by

Let the radius of the 2nd sphere be denoted by

We know that the surface area of any sphere with radius,r is given by the formula: where S is the surface area.

Now, let the surface area of the 1st sphere be represented by . Therefore,

Likewise, for the second sphere we will have:

Now, we have been given that:

Now, we know that the Volume, V of any sphere of radius,r is given by the formula:

Thus, the ratio of the volumes of the 1st and the 2nd spheres will be given by:

(where symbols have their usual meanings)

Therefore,

Thus, the ratio of their volumes is

the correct answer is 5