The volume of a cone is 25/3 * pi*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? (1point)
The volume of a cone is given by the formula:
V(cone) = (1/3) * pi * r^2 * h
where r is the radius and h is the height of the cone.
Given that the volume of the cone is:
V(cone) = 25/3 * pi cm^3
Since the height of the cone is equal to the diameter of the sphere, and the radius of the cone is the same as the sphere's radius, we have:
h(cone) = 2r(cone)
So, we can rewrite the formula for the volume of the cone as:
V(cone) = (1/3) * pi * r(cone)^2 * 2r(cone)
25/3 * pi = (1/3) * pi * r(cone)^2 * 2r(cone)
Simplifying the equation, we get:
25 = 2 * r(cone)^3
r(cone)^3 = 25/2
Since the radius of the cone is the same as the radius of the sphere, we can find the volume of the sphere using the formula:
V(sphere) = (4/3) * pi * r(sphere)^3
Substituting the value of r(sphere) with the cube root of (25/2), we can calculate the volume of the sphere:
V(sphere) = (4/3) * pi * (25/2)^(1/3)
Therefore, the volume of the sphere is (4/3) * pi * (25/2)^(1/3) cm^3.