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
25 π cm3
25 pi cm cubed
503 π cm3
Start Fraction 50 over 3 End Fraction pi cm cubed
252 π cm3
The volume of a cone is given by the formula (1/3)πr^2h, where r is the radius and h is the height. The radius of the cone and the sphere are the same, so let's call it r. The height of the cone is equal to the sphere's diameter, which is 2r.
Substituting these values into the formula for the volume of the cone, we get:
(1/3)πr^2(2r)
Simplifying, we get:
(2/3)πr^3
We are given that the volume of the cone is 253π cm^3, so we can set up the equation:
(2/3)πr^3 = 253π
Now we can solve for r:
r^3 = (253 * 3) / 2
r^3 = 379.5
r = ∛379.5
Now we can find the volume of the sphere using the formula (4/3)πr^3:
(4/3)π(∛379.5)^3
Simplifying, we get:
(4/3)π * 379.5
The final answer is approximately 503π cm^3. So the correct option is 503π cm^3.