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.)