Question

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

Answer 1

$\bf \textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}\qquad \begin{cases} B=\textit{area of its base}\\ h=height\\ ----------\\ B=\stackrel{square~pyramid}{length\cdot width}\\ \qquad s\cdot s\\ \qquad s^2\\ h=\frac{2}{3}s \end{cases}\implies V=\cfrac{s^2\cdot \frac{2s}{3}}{3} \\\\\\ V=\cfrac{\frac{2s^3}{3}}{3}\implies V=\cfrac{\frac{2s^3}{3}}{\frac{3}{1}}\implies V=\cfrac{2s^3}{3}\cdot \cfrac{1}{3}\implies V=\cfrac{2s^3}{9}$