The surface area of the first ball is 36 times the surface area of the second ball.

The surface area of the first ball is 36 times the surface area of the second ball. Find how many times the volume of the first ball is greater than the volume of the second ball?

We denote the surface area of the first ball S1, the second – S2, then we write down what they equal, for radii r and R:
S1 = 4πr ^ 2;
S2 = 4πR ^ 2.
Area Ratio:
S1: S2 = 4πr ^ 2 / 4πR ^ 2 = r ^ 2 / R ^ 2 = 36.
r = 6R.
We can conclude that the radius of the first ball is six times larger than the second, then the volume ratio will look like:
V1 = (4/3) * r ^ 3 * π = (4/3) * 216R ^ 3 * π;
V2 = (4/3) * R ^ 3 * π;
V1 / V2 = (4/3) * 216R ^ 3 * π / (4/3) * R ^ 3 * π = 216.
Answer: The volume of the first ball is 216 times greater than the volume of the second ball.