as already mentioned, the volume for a rectangular prism, namely a box in this case, is just the product of its dimensions, length * width * height.
[tex]\bf \textit{volume of a rectangular prism}\\\\
V=LWH\quad
\begin{cases}
L=length\\
W=width\\
H=height\\
------\\
L=3\\
W=2\\
H=5\frac{1}{2}
\end{cases}\implies V=3\cdot 2\cdot 5\frac{1}{2}
\\\\\\
V=3\cdot 2\cdot \cfrac{5\cdot 2+1}{2}\implies V=6\cdot\cfrac{11}{2}\implies V=3\cdot \cfrac{11}{1}
\\\\\\
V=33[/tex]
now, as far as another one... hmm is easier if you post in the channel, that way I can include any graphs if needed or tables and such.
so, what happens if you double up the dimensions?
[tex]\bf \textit{volume of a rectangular prism}\\\\
V=LWH\quad
\begin{cases}
L=length\\
W=width\\
H=height\\
------\\
L=6\\
W=4\\
H=10
\end{cases}\implies V=6\cdot 4\cdot 10\implies V=240\\\\
-------------------------------\\\\
\begin{cases}
L=6(2)\\
W=4(2)\\
H=10(2)
\end{cases}\implies V=6(2)8(2)10(2)\implies V=(2)(2)(2)6\cdot 8\cdot 10
\\\\\\
V=(8)6\cdot 8\cdot 10\implies V=(8)\stackrel{original~volume}{240}[/tex]
notice, how many times the new size is, is 8 times the original.
