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)

256 π cm3


25 π cm3


252 π cm3


503 π cm3

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Answer 1

Let r be the common radius. The cone’s height is the sphere’s diameter, so h = 2r.

V_cone = (1/3)πr^2h = (1/3)πr^2(2r) = (2/3)πr^3.

V_sphere = (4/3)πr^3.

So V_sphere / V_cone = ((4/3)πr^3)/((2/3)πr^3) = 2, hence V_sphere = 2·V_cone.

Given V_cone = 253π cm^3, V_sphere = 2·253π = 506π cm^3.

None of the provided choices match 506π.