Question

The volume of a pyramid that fits exactly inside a cube is 49 cubic feet. What is the volume of the cube?

Answer 1

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.