What is the formula for the volume of a pyramid with base area B and height h?

• A. B h
• B. 1/2 B h
• C. 1/3 B h
• D. 3 B h

Answer: (C)

A pyramid’s volume comes from how its cross-sections shrink as you move from the base to the apex. If you imagine slicing the pyramid with planes parallel to the base, each slice gets smaller in area as you go up, and that shrinking follows a square relationship with distance from the base. When you sum all those slices, the total volume works out to one-third of the product of the base area and the height. So with base area B and height h, the volume is (1/3) B h. This is smaller than the prism with the same base and height, which would have volume B h, and why the factor is one-third rather than one-half or three.