What is the diameter of a sphere whose volume is equal to its surface area?

We will use the formulas for the volume of a ball and its surface area, equate them and find the diameter of the ball.
V = 4/3 * π * R³;
S = 4 * π * R².
V = S → 4/3 * π * R³ = 4 * π * R².
4 * π * R³ = 12 * π * R².
R = 3.
The radius of the ball is known, then the diameter will be equal to:
D = 2R = 6.
Answer: a sphere whose volume and surface area are equal has a diameter of 6 units.