Let R be each side of the base and H is the height. Take a slice of the pyramid of thickness dh and length r at a height h from the vertex.
The volume of this slice is
dV = r^2*dh.By simple geometry you can see that R/H = r/h.
r = (R/H)*h.
dV = (R/H)^2*h^2*dh.
To find the total volume find the integration between h = 0 to h = H.