Find the diameter of a sphere whose volume is equal to the volume of a cone with a height of 2 and a radius of 4.

The volume of the cone is V con. = 1/3 П R² H, where R is the radius of the base of the cone, H is the height of the cone;

Vcon. = 1/3 P * 16 * 2 = 1/3 * 32 P;

The volume of the ball V of the ball = 1 1/3 П R³, where R is the radius of the ball; By condition, the volume of the ball is equal to the volume of the cone, therefore:

1 1/3 P R³ = 1/3 * 32P;

4/3 P R³ = 32/3 P;

R³ = 32/3: 4/3; R³ = 8; R = 2;

Answer: the radius of the ball is 2.