The volume of a sphere is 72 m3 . 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?(1 point) m3

Answer 1

To find the volume of the cone, you can first calculate the radius and height of the cone using the information provided.

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

Given that the volume of the sphere is 72 m^3, we can rearrange the formula to solve for the radius:
72 = (4/3) * π * r^3
r^3 = (3/4) * (72/π)
r = (3/4) * (72/π)^(1/3)
r ≈ 2.88 m

Since the radius of the cone is the same as the sphere, the radius of the cone is also 2.88 m.

The height of the cone is equal to the sphere's diameter, which is twice the radius of the sphere:
h = 2 * r
h = 2 * 2.88
h ≈ 5.76 m

Now, you can calculate the volume of the cone using the formula:
V_cone = (1/3) * π * r^2 * h
V_cone = (1/3) * π * 2.88^2 * 5.76
V_cone ≈ 55.36 m^3

Therefore, the volume of the cone is approximately 55.36 m^3.