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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's denote the radius of the sphere as r and the height of the cone as 2r (equal to the sphere's diameter).

The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * r^3

Given that the volume of the sphere is 72 m^3, we can set up the equation:
72 = (4/3) * π * r^3

Rearranging the equation, we have:
r^3 = (3/4) * (72 / π)
r^3 ≈ 54.94

Taking the cube root of both sides:
r ≈ 3.83

Now, let's find the volume of the cone:
The volume of a cone is given by the formula:
V_cone = (1/3) * π * r^2 * h

Since the radius of the cone is the same as the sphere's (r ≈ 3.83) and the height of the cone is 2r (2 * r ≈ 7.66), we can substitute the values into the formula:
V_cone = (1/3) * π * (3.83)^2 * 7.66
V_cone ≈ 115.07 m^3

Therefore, the volume of the cone is approximately 115.07 m^3.