Some general principles: Suppose and are two similar figures. Assume that the ratio of two corresponding one-dimensional lengths is a/b. Then the ratio of two corresponding two-dimensional areas is , and the ratio of two corresponding three-dimensional volumes is .
The volume of a prism with base of area B and height h is Bh (area of base times height).
The volume of a pyramid with base of area A and height h is . You can prove this with calculus by placing the pyramid with apex at the origin and with base perpendicular to the z-axis. Then we can calculate the volume by making slices perpendicular to the z-axis. Let A(z) be the area of the slice at position z. Then , so . We get the volume by integrating from z=0 to z=h: