The volume of a pyramid is given by the formula

Volume = 1/3*height*(area of base)

In calculus terms, the volume is the integral over the height of

volume = integral over 0 to h of (y/h)^2*(base area)(dy)

= (1/(3*h^2))(base area)(h^3) = (1/3)*h*(base area)

(For those paying attention, this is actually the computation of the volume of an inverted pyramid, one whose apex is found at y=0, and whose base is found at y=h. The math is much simpler and the result is the same as if the pyramid were base-down.)

Volume = 1/3*height*(area of base)

In calculus terms, the volume is the integral over the height of

volume = integral over 0 to h of (y/h)^2*(base area)(dy)

= (1/(3*h^2))(base area)(h^3) = (1/3)*h*(base area)

(For those paying attention, this is actually the computation of the volume of an inverted pyramid, one whose apex is found at y=0, and whose base is found at y=h. The math is much simpler and the result is the same as if the pyramid were base-down.)