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 25 π cm3 25 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 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 of the cone is equal to the sphere's diameter, we can express the volume of the cone in terms of the sphere's radius (which is also the cone's radius) and height:
253π = (1/3)π(r^2)(2r)
Simplifying, we get:
253 = (2/3)r^3
To find the volume of the sphere with the same radius as the cone, we use the formula V = (4/3)πr^3.
V = (4/3)π(r^3) = (4/3)π (253) ≈ 337π cm^3
Therefore, the volume of the sphere with the same radius as the cone and the height equal to the sphere's diameter is approximately 337π cm^3.