The volume of the cube is 48. Find the volume of the pyramid, the base of which is the face

The volume of the cube is 48. Find the volume of the pyramid, the base of which is the face of the cube and the top is the center of the cube.

The volume of the cube is equal to a ^ 3, where a is the edge of the cube. By the condition of the problem, a ^ 3 = 48. The volume of the pyramid is equal to a third of the product of its base by the height: V = (1/3) * S * h. The base of this pyramid is equal to the side of the cube, which means S = a ^ 2, its height is equal to half the length of the edge of the cube, i.e. h = a / 2.
Thus, the volume of the pyramid is V = (1/3) * S * h = (1/3) * (a ^ 2) * (a / 2) = a ^ 3/6 = 48/6 = 8.