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 volume of a sphere is given by V = (4/3)πr³, where r is the radius.
So we have:
72 = (4/3)πr³
r³ = (3/4) * (72/π)
r = (3/4) * (72/π)^(1/3) ≈ 2.547 m
The diameter of the sphere is simply 2 times the radius, so the diameter is:
2 * 2.547 = 5.094 m
Now, the height of the cone is equal to the sphere's diameter, which is 5.094 m.
The volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height.
Since the radius of the cone is the same as the sphere, r = 2.547 m and the height is 5.094 m, we have:
V = (1/3)π(2.547)² * 5.094 ≈ 26.214 m³
Therefore, the volume of the cone is approximately 26.214 m³.