Question

The volume of a cone is 253 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

25 π cm3

25 pi cm cubed

256 π cm3

Start Fraction 25 over 6 End Fraction pi cm cubed

503 π cm3

Start Fraction 50 over 3 End Fraction pi cm cubed

252 π cm3

Answer 1

Let r be the common radius and h the cone height. Cone: (1/3)πr^2h = 253π → r^2h = 759.
Given h = 2r, so 2r^3 = 759 → r^3 = 759/2.
Sphere volume: (4/3)πr^3 = (4/3)π(759/2) = 506π cm^3.

So the correct volume is 506π cm^3 — none of the provided choices match.