Which expression correctly gives the volume of a pyramid with base area B and height h?

Which expression correctly gives the volume of a pyramid with base area B and height h?

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

Answer: (A)

The volume of a pyramid comes from taking one third of the product of its base area and its height. If you imagine a prism with the same base and height, the pyramid fits inside and fills exactly one third of that prism, which is why the factor is 1/3. With base area B and height h, the amount of space inside the pyramid is (1/3) × B × h. This is the standard way to write it, and it matches the idea that the pyramid is one third of the corresponding prism. Bh would describe the volume of a prism, not a pyramid, so it’s too large for this shape. Three times Bh would be even larger. Writing it as h/3 × B is the same value as (1/3)Bh; it’s just another way to order the factors, but the key idea remains: one third of Bh.

The volume of a pyramid comes from taking one third of the product of its base area and its height. If you imagine a prism with the same base and height, the pyramid fits inside and fills exactly one third of that prism, which is why the factor is 1/3.

With base area B and height h, the amount of space inside the pyramid is (1/3) × B × h. This is the standard way to write it, and it matches the idea that the pyramid is one third of the corresponding prism.

Bh would describe the volume of a prism, not a pyramid, so it’s too large for this shape. Three times Bh would be even larger. Writing it as h/3 × B is the same value as (1/3)Bh; it’s just another way to order the factors, but the key idea remains: one third of Bh.