The volume of a sphere is given by the formula V = (4/3)Ï€r^3, where r is the radius of the sphere.
Given that the volume of the sphere is 72m^3, we can solve for the radius of the sphere:
72 = (4/3)Ï€r^3
72 = (4/3)(3.14159)(r^3)
72 = 4.18879r^3
r^3 = 72 / 4.18879
r^3 = 17.1867
r = ∛(17.1867)
r ≈ 2.65m
Now, the volume of a cone is given by the formula V = (1/3)Ï€r^2h, where r is the radius of the cone and h is the height of the cone.
Since the cone has the same radius as the sphere and the height is equal to the diameter (2r), we have:
r = 2.65m
h = 2r = 2(2.65) = 5.3m
Now, we can calculate the volume of the cone:
V = (1/3)Ï€(2.65)^2(5.3)
V = (1/3)(3.14159)(7.0225)(5.3)
V = (1/3)(3.14159)(37.16925)
V ≈ 39.2m^3
Therefore, the volume of the cone is approximately 39.2m^3.