[tex]\bf \textit{volume of a rectangular prism}\\\\
V=\stackrel{length}{L}\cdot \stackrel{width}{w}\cdot \stackrel{height}{h}\qquad
\begin{cases}
L=2L\\
w=2w\\
h=3h
\end{cases}\implies V=(2L)(2w)(3h)
\\\\\\
V=12Lwh\impliedby \stackrel{original~volume}{\underline{Lwh}}\qquad \qquad \stackrel{dilated~volume}{12 \underline{Lwh}}[/tex]
notice the new volume is that many times more than the original.
