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 503 π cm3 Start Fraction 50 over 3 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 256 π cm3
The volume of a cone is given by the formula 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, and the height is equal to the sphere's diameter, we can set up the following equation:
253π = (1/3)πr^2(2r)
Solving for r, we get r = 5.
Now, the volume of a sphere is given by the formula V = (4/3)πr^3. Substituting the radius of the cone (r = 5) into this formula, we get:
V = (4/3)π(5)^3
V = (4/3)π*125
V = 500π/3 = 166.67π cm^3
Therefore, the volume of the sphere is 167π cm^3.
So the answer is 503π cm3.