Derive the formula for the volume of a truncated right pyram

Derive the formula for the volume of a truncated right pyramid (a \"frustum\") by Subtracting the volume of the \"cut off\" pyramid from the volume of the original Pyramid. You may use the fact that the volume of a pyramid is V = 1/3 b^2H Your formula should involve only a, b, and h (*not* H).

Solution

Volume of the bigger pyramid = 1/3 * b^2H

Volume of the smaller pyramid = 1/3 * b^2h

Volume of the remaining object = 1/3 * b^2 * (H - h)

assuming the similarlity we can write

h/H = a/b

H = hb/a

substituting the values we get

Volume of the remaining object = 1/3 * b^2 * (hb/a - h)

=> 1/3 * b^2 * h(b-a)/a = 1/3 * b^2 * (b-a)/a * h