Question

The volume of a sphere is 72 m^3 . What is the volume of a cone if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter? whats the exact answer

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to find the radius of the sphere. The formula for the volume of a sphere is:

V = (4/3)πr^3

Given that the volume of the sphere is 72 m^3, we can rearrange the formula to solve for the radius:

72 = (4/3)πr^3
r^3 = 27/(4π)
r = (27/(4π))^(1/3)
r ≈ 2.63 m

Therefore, the radius of the sphere is approximately 2.63 m.

Next, we need to find the volume of the cone. The formula for the volume of a cone is:

V = (1/3)πr^2h

Since the radius of the cone is the same as the radius of the sphere and the height of the cone is equal to the diameter of the sphere, the height of the cone is twice the radius of the sphere:

h = 2(2.63) = 5.26 m

Now we can plug in the values into the formula for the volume of the cone:

V = (1/3)π(2.63)^2(5.26)
V = (1/3)π(6.92)(5.26)
V = (1/3)π(36.35)
V ≈ 38.16 m^3

Therefore, the volume of the cone is approximately 38.16 m^3.