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

7 cubic feet

147 cubic feet

241 cubic feet

2401 cubic feet

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.