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?
the answer has to be in fraction form can you put the answer in fraction form
The volume of a cone is given by the formula V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
Given that the volume of the cone is 253π cm^3, we have:
253π = (1/3)πr^2h
Since the height of the cone is equal to the sphere's diameter, we have h = 2r.
Substituting h = 2r into the equation, we get:
253π = (1/3)πr^2(2r)
Simplifying, we have:
253π = (2/3)πr^3
Dividing both sides by (2/3)π, we get:
253 = r^3
Taking the cube root of both sides, we have:
r = 6.25
The radius of the sphere is also r = 6.25.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
Substituting r = 6.25 into the formula, we get:
V = (4/3)π(6.25)^3
Simplifying, we have:
V ≈ 651.0417π
Therefore, the volume of the sphere is approximately 651.0417π cm^3.