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Find the volume of the composite solid.

Find the volume of the composite solid.-example-1
User Jeisson
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Check the picture below.

so we have a cube with a pyramidical hole, so let's just get the volume of the whole cube and subtract the volume of the pyramid, what's leftover is the part we didn't subtract, the cube with the hole in it.


\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{6√(2)* 6√(2)}{72}\\ h=12 \end{cases}\implies V=\cfrac{72\cdot 12}{3}\implies 288 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE volumes} }{\stackrel{ cube }{12^3}~~ - ~~\stackrel{ pyramid }{288}}\implies \text{\LARGE 1440}~in^3

Find the volume of the composite solid.-example-1
User Guanhuiwit
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