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?

Answer 1

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.

Answer 2

the answer has to be in fraction form can you put the answer in fraction form