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)
First, we need to find the radius and diameter of the sphere.
The formula for the volume of a sphere is:
V_sphere = 4/3 * π * r^3
Given that V_sphere = 72 m^3, we can rearrange the formula to solve for the radius (r):
72 = 4/3 * π * r^3
r^3 = 72 / (4/3 * π)
r = (3 * 72 / (4 * π))^(1/3)
r ≈ 2.3437 m
The diameter of the sphere is twice the radius:
Diameter = 2 * r ≈ 4.6874 m
Now, we can use the formula for the volume of a cone:
V_cone = 1/3 * π * r^2 * h
Since the radius of the cone is the same as the sphere's radius and the height is equal to the sphere's diameter, we have:
V_cone = 1/3 * π * (2.3437)^2 * 4.6874
V_cone ≈ 72 m^3
Therefore, the volume of the cone with the given dimensions is approximately 72 m^3.