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 25 π cm3 25 pi cm cubed 503 π cm3
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the volume of the cone is 253π cm^3, we can rearrange the formula to solve for h:
253π = (1/3)πr^2h
h = 253 * 3 / r^2
We are also given that the height of the cone is equal to the sphere's diameter, so h = 2r.
Substituting this into the formula for h, we get:
2r = 253 * 3 / r^2
2r^3 = 253 * 3
2r^3 = 759
r^3 = 759/2
r^3 = 379.5
r ≈ 7.42 cm
The formula for the volume of a sphere is V = (4/3)πr^3. Substituting the value of r, we get:
V = (4/3)π(7.42)^3
V ≈ 256π cm^3
Therefore, the volume of the sphere is 256π cm^3.