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.
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)
1 answer
1 answer