Question

A pyramid has a square base with side s. The height of the pyramid is 2/3 that of its side. What is the expression for the volume of the pyramid?

Answer 1

Well, this is a bit confusing. I think the height is 2/3 that of a side of the base. If that is correct, then the height is h = 2/3s. The formula for the volume of a pyramid is \[V=\frac{ 1 }{ 3 }s ^{2}h\]Normally it would be "B" for base area, but since this is a square and the height is in terms of "s", that would be the formula. If we find the area based on the fact that h = 2/3s, then it appears that the formula would be\[V=\frac{ 1 }{ 3 }s ^{2}(\frac{ 2 }{ 3 }s)\]If you multiply that all out, it would be \[V=\frac{ 2 }{ 9 }s ^{3}\]That seems a bit strange, doesn't it?