Question

Find the volume to the nearest whole number.

Answer 1

well, we know the base is an equalateral triangle and the height of the pyramid is 15 cm, so

`\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2√(3)}{4} ~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2√(3)}{4} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ h=15\\\\ B=(12^2√(3))/(4) \end{cases}\implies V=\cfrac{1}{3}\cdot \cfrac{12^2√(3)}{4}\cdot 15\implies V\approx 312~cm^2`