The volume of a pyramid is given by which expression?

• A. Base Area × h
• B. 1/3 × Base Area × h
• C. Base Area + h
• D. Base Area ÷ h

Answer: (B)

A pyramid’s volume is one third of the prism that has the same base and the same height. Picture the space the pyramid occupies: if you imagine a prism using the same base shape and height, its volume would be Base Area × height. As you move from the base up toward the apex, the cross-sectional areas shrink in a way that makes the total volume exactly one third of that prism. A quick way to see this is by integrating the cross-sectional area that scales like (1 − z/h)² from z = 0 to z = h, which yields V = (1/3) × (Base Area) × height. So the correct expression for the volume is (1/3) × (Base Area) × h. The other forms don’t match the geometric relationship: base area times height gives a prism’s volume, while adding or dividing doesn’t produce the correct units or result.