Answer: 32π cubic inches.
Explanation:
Both cones have the same volume because the volume of a cone depends on both its height and radius, not just one or the other. However, the formula for the volume of a cone is V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height. So we can calculate the volumes of each cone to confirm that they are indeed equal:
Cone 1 with height of 6 inches and radius of 4 inches:
V = (1/3)π(4²)(6) = 32π
Cone 2 with height of 4 inches and radius of 6 inches:
V = (1/3)π(6²)(4) = 32π
Therefore, both cones have the same volume of 32π cubic inches.