Question

The volume of a cone is 2/53 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

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

256 π cm3

Answer 1

Let the common radius be r. Cone: V_cone = (1/3)πr^2h and h = 2r, so V_cone = (2/3)πr^3. Sphere: V_sphere = (4/3)πr^3 = 2·(2/3)πr^3 = 2·V_cone.

Thus V_sphere = 2·(25/3)π = 50/3 π cm^3.