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

252 π cm3
Start Fraction 25 over 2 End Fraction pi cm cubed

503 π cm3
Start Fraction 50 over 3 End Fraction pi cm cubed

25 π cm3
25 pi cm cubed

256 π cm3

Answer 1

Let the cone's radius be r and height h. Cone volume: (1/3)πr^2h = (25/3)π, so r^2h = 25. Given h = 2r, so r^2(2r) = 25 ⇒ 2r^3 = 25 ⇒ r^3 = 25/2. Sphere volume: (4/3)πr^3 = (4/3)π(25/2) = (50/3)π cm^3.

Answer: (50/3)π cm^3.