an image shows three objects, a cone a cylinder and a sphere, the cone has a height of 3r and the cylinder also has a height of 3r.

Question

the volume of the cone is 25(pi) using this information, answer the question below:

The volume of the sphere if the radius is the same value as the cone.

Possible answers: A: 3R B: 100/3(PI) C: 75/2(PI) D: 75(PI) E: 1/3 F: 25(PI) G: 3 H: 4R I: 125(PI) J: 50/3(PI) K: 2

Answer 1

J: 50/3(PI)

The volume of a cone is given by the formula V = (1/3)πr^2h, with r as the radius and h as the height. Since the volume of the cone is 25π and the height is 3r, we can set up the equation:

(1/3)πr^2(3r) = 25π
r^2(3r) = 75
r^3 = 75/3
r^3 = 25
r = ∛25
r = 25^(1/3)

The volume of a sphere is given by the formula V = (4/3)πr^3. Substituting r = 25^(1/3) into the formula, we get:

V = (4/3)π(25^(1/3))^3
V = (4/3)π(25)
V = 100/3π
V = 50/3(π)

Therefore, the volume of the sphere with radius equal to the cone is 50/3(π), which corresponds to answer J.