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?

Question

imstuck · Answer

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?