What formula calculates the volume of a pyramid?

The formula for calculating the volume of a pyramid is given by V = 1/3 (lwh), where 'l' represents the length of the base, 'w' represents the width of the base, and 'h' represents the height of the pyramid. This formula is derived from the geometric principles that relate the volume of pyramids to that of prisms.

In essence, the formula reflects that the volume of a pyramid is one-third the product of the base area and the height. This relationship is consistent across pyramids with different base shapes, as long as you consider the base area and height accordingly. Since the pyramid tapers to a point, it occupies less volume than a prism that has the same base area and height.

The other options represent formulas for different geometric shapes. The choice involving πr²h calculates the volume of a cylinder, while 4/3πr³ gives the volume of a sphere. The final option, 1/2 bh, represents the area of a triangle and not a volume, as it does not incorporate the three-dimensional aspect necessary for volume calculation. Therefore, the formula for the volume of a pyramid is accurately captured by V = 1/3 (lwh).