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

256 π cm3

Start Fraction 25 over 6 End Fraction 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

25 π cm3

25 pi cm cubed
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Answer 1

Let r be the common radius and h the cone’s height. With h = 2r,
V_cone = (1/3)π r^2 h = (1/3)π r^2(2r) = (2/3)π r^3.
V_sphere = (4/3)π r^3 = 2·(2/3)π r^3 = 2·V_cone.

So V_sphere = 2·253π = 506π cm^3.

(None of the given choices equals 506π.)