What formula is used to calculate the volume of a pyramid?

The volume of a pyramid is calculated using the formula that involves one-third of the product of the base area and the height of the pyramid. This formula reflects the geometric property that a pyramid’s volume is one-third that of a prism with the same base area and height.

To understand why this formula holds, consider that a pyramid has a single apex from which all the triangular faces converge to meet. When compared to a rectangular prism, which has parallel top and bottom faces, the pyramid's volume is less due to the tapering shape. The fraction of one-third accounts for the geometric relationship between the height and the area of the base, effectively summarizing the way the space inside the pyramid is filled as you move from the base to the apex. Thus, the correct formula for finding the volume of a pyramid confirms this unique structure's properties in comparison to other three-dimensional shapes.