Question

The volume of a cube is 36 cubic feet. What is the volume of a pyramid that fits exactly inside the cube? Provide an explanation and proof for your answer to receive full credit.

Answer 1

Volume of a cube : V = a³ = 36 ft³
Volume of a pyramid:
V = 1/3 * B * h
If a pyramid fits exactly inside the cube:
B = a² and h = a.
V = 1/3 * a² * a = 1/3 a³ = 1/3 * Volume of a cube
V (pyramid ) = 1/3 * 36 = 12 ft³