Question

The volume of a cone is 25/3 π cm3
. What is the volume of a sphere if its radius is the same as the cone’s and the height of the cone is equal to the sphere’s diameter?(1 point)
Responses

50/3 π cm3

25 π cm3

25/2 π cm3

25/6 π cm3

Answer 1

Cone: V = (1/3)πr^2h and h = 2r, so V = (1/3)πr^2(2r) = (2/3)πr^3 = 25/3 π.
Thus 2r^3 = 25 → r^3 = 25/2.

Sphere: V = (4/3)πr^3 = (4/3)π(25/2) = 50/3 π cm^3.

Answer: 50/3 π cm^3.