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?(1 point)
First, we need to find the radius of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius.
Given that the volume of the sphere is 72 m^3, we can plug in the values into the formula:
72 = (4/3)πr^3
r^3 = (3/4)(72/π)
r = ∛(54/π)
r ≈ 2.68 m
Next, we need to find the height of the cone, which is equal to the diameter of the sphere. Since the diameter is twice the radius, the height of the cone would be 2 * 2.68 = 5.36 m.
Now, we can use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the radius and h is the height. Plug in the values:
V = (1/3)π(2.68)^2(5.36)
V = (1/3)π(7.1824)(5.36)
V ≈ 40.525 m^3
Therefore, the volume of the cone with the same radius as the sphere and a height equal to the sphere's diameter is approximately 40.525 m^3.