How many times will the volume of the sphere increase if its diameter is increased 5 times?

Let us determine how many times the volume of the sphere will increase if its diameter is increased by 5 times.

Let’s write down the formula for the volume of the ball:

V = 4/3 * pi * R ^ 3;

The diameter increases 5 times and is equal to d = 5 * R, then the radius of the ball increases by R = d / 2 = 5 * R / 2 = 2.5 * R times.

Let’s find now the volume of the ball, after increasing the diameter of the ball.

V = 4/3 * pi * (2.5 * R) ^ 3 = 2.5 ^ 3 * 4/3 * pi * R ^ 3 = 15.625 * 4/3 * pi * R ^ 3;

Hence we see that if the diameter is increased by 5 times, then the volume of the sphere will increase by 15.625 times.

Answer: the volume of the ball will increase by 15.625 times.