Question

Find the volume of the solid brow, composed of two pyramids connected by the same vertical square base

Answer 1

Check the picture below.

so we can simply get the volume of each and sum them up.

$\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}~~ \begin{cases} h=height\\ B=base's~area\\[-0.5em] \hrulefill\\ h=6\\ B=\stackrel{8\times 8}{64} \end{cases}\implies V=\cfrac{(64)(6)}{3}\implies V=128$

$\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}~~ \begin{cases} h=height\\ B=base's~area\\[-0.5em] \hrulefill\\ h=12\\ B=\stackrel{8\times 8}{64} \end{cases}\implies V=\cfrac{(64)(12)}{3}\implies V=256 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 128~~ + ~~256~~ = ~~384~\hfill$