If the pyramid fits perfectly in a cube, this means that its base is a square and its height has the same value as the side of the square. Let x be the measure of the sides of the cube. The volume of the cube (Vc),
Vc = x³ ; 49 ft³ = x³ ; x = 49^(1/3)
The volume of the pyramid is,
Vp = (1/3)(x²)(x) = (1/3)(x³)
Substituting the known values,
Vp = (1/3)((49^(1/3))³ = 16 1/3 ft³
Thus, the volume of the pyramid is approximately 16.33 ft³.
