What is the formula for the volume of a pyramid?

The formula for the volume of a pyramid is derived from the geometric properties of pyramids and the relationship between the base area and the height. The correct answer emphasizes that to calculate the volume of a pyramid, one must first find the area of the base. This area is then multiplied by the height of the pyramid, and since a pyramid is essentially a three-dimensional object that tapers to a point, the final volume is one-third of this product.

This relationship arises because the volume of a pyramid can be visualized as being formed from a prism with the same base and height. A prism has a volume equal to the base area multiplied by the height. However, a pyramid occupies only a fraction of that space, specifically one-third, due to its tapering shape which reduces the amount of volume it contains compared to the prism.

Thus, the formula is stated as one-third times the area of the base times the height, accurately reflecting the volume of a pyramid in three-dimensional space.