The volume of a cone is 25/3 π cm^3 . 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)
50/3 pi cm^3
25 pi cm^3
25/2 pi cm^3
25/0 pi cm^#
The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Given that the volume of the cone is 25/3 π cm^3, and the height of the cone is equal to the sphere's diameter, we can say that h = 2r.
Substituting this value into the volume formula, we have 25/3 π = (1/3) * π * r^2 * (2r).
Simplifying the equation, we get 25/3 = 2r^3.
Dividing both sides by 2 to isolate r^3, we have 12.5/3 = r^3.
Taking the cube root of both sides, we find r ≈ 2.08 cm.
Now, the volume of a sphere is given by the formula V = (4/3) * π * r^3.
Substituting the value of r, we have V = (4/3) * π * (2.08)^3.
Calculating this, we find V ≈ 50/3 π cm^3.
Therefore, the volume of the sphere is 50/3 π cm^3.