By definition, you know that the volume of a rectangular prism is given by the formula
[tex]\begin{gathered} V=l\cdot w\cdot h \\ \text{ Where} \\ l=\text{length} \\ w=\text{width} \\ h=\text{height} \end{gathered}[/tex]So, you can make a drawing to understand the procedure easier
Then you have
[tex]\begin{gathered} V=l\cdot w\cdot h \\ 162=l\cdot\frac{l}{2}\cdot3w \\ 162=l\cdot\frac{l}{2}\cdot3(\frac{l}{2}) \\ 162=l\cdot\frac{l}{2}\cdot\frac{3l}{2} \\ 162=\frac{3l^3}{4} \\ \text{ Multiply both sides of the equation by }4 \\ 162\cdot4=\frac{3l^3}{4}\cdot4 \\ 648=3l^3 \\ \text{ Divide both sides of the equation by 3} \\ \frac{648}{3}=\frac{3l^3}{3} \\ 216=l^3 \\ \text{ Apply cube root to both sides of the equation} \\ \sqrt[3]{216}=\sqrt[3]{l^3} \\ 6=l \end{gathered}[/tex]And so, for the other dimensions, you get
[tex]\begin{gathered} w=\frac{l}{2} \\ w=\frac{6}{2} \\ w=3 \end{gathered}[/tex][tex]\begin{gathered} h=3\cdot w \\ h=3\cdot3 \\ h=9 \end{gathered}[/tex]Therefore, the dimensions of the rectangular prism are 6 meters in length, 3 meters in width, and 9 meters height.
