Compute the volume of a frustum of a pyramid with square bas

Compute the volume of a frustum of a pyramid with square base of side b, squaretop of side a, and height h

Solution

As we are given square base of side b , square top of side a and height h, so we will have

Then its volume V = b²H

The frustum is this pyramid with a smaller pyramid of altitude Hh cut off the top.

The similarity ratio for these two pyramids is a/b

Volume of frustum = b²H b²H.(a/b)³ = b²H{1(a/b)³}

But by the similarity property (H-h)/H = a/b H = hb/(b-a)

Hence Volume = hb³(1(a/b)³)/(b-a)

Now b³(1(a/b)³)/(b-a) = ( b³a³) /(b-a) = b²+ab+a²

Volume = h(b²+ab+a²)    answer