The volume of one ball is 7 times the volume of the second.

The volume of one ball is 7 times the volume of the second. How many times is the surface area of the first ball greater than the surface area of the second?

1. To compare two different volumes of different balls, we write down the formulas of these values for each of them:

V1 = 4/3 * п * R1³

V2 = 4/3 *п * R2³

By the condition of the problem V1: V2 = 7, it means (4/3 * п * R1³): (4/3 * п * R2³) = R1³: R2³ = 7,

that is, R1: R2 = 7 ^ 1/3

To compare the areas of surfaces of two balls, we will use the formulas

S1 = 4 * п * R1² and S2 = 4 * п * R2² whence their ratio is

S1: S2 = (4 * R * R1²): (4 * R * R2²) = R1²: R2² = (R1: R2) ².

And it means S1: S2 = (7 ^ 1/3) ² = 49 ^ 1/3 = 3.66.

Answer: The surface areas of the balls differ by a factor of 3.66.