The cone is inscribed in the ball. the radius of the base of the cone is equal to the radius of the ball

The cone is inscribed in the ball. the radius of the base of the cone is equal to the radius of the ball. the volume of the cone is 27. Find the volume of the ball.

Since, by condition, the radius of the ball and the radius of the cone are equal, this is possible if the base of the cone coincides with the axial section of the ball. Then the height of the VO of the cone is equal to the radius of the ball and the radius of the circle at the base of the cone.

Let’s use the formulas for the volume of the cone:

Vfin = Sbasn * VO / 3 = π * R ^ 2 * BO / 3 = π * R ^ 3/3 = 27 cm3.

R ^ 3/3 = 27 / π.

Then the volume of the ball is:

Vball = 4 * π * R ^ 3/3 = 4 * π * (27 / π) = 4 * 27 = 108 cm3.

Answer: The volume of the ball is 108 cm3.