Question

A packing box has the dimensions 3 by 2 by 5 1/2 feet. What is the volume of the box?

Answer 1

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.

$\bf \textit{volume of a rectangular prism}\\\\ V=LWH\quad \begin{cases} L=length\\ W=width\\ H=height\\ ------\\ L=3\\ W=2\\ H=5\frac{1}{2} \end{cases}\implies V=3\cdot 2\cdot 5\frac{1}{2} \\\\\\ V=3\cdot 2\cdot \cfrac{5\cdot 2+1}{2}\implies V=6\cdot\cfrac{11}{2}\implies V=3\cdot \cfrac{11}{1} \\\\\\ V=33$

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?

$\bf \textit{volume of a rectangular prism}\\\\ V=LWH\quad \begin{cases} L=length\\ W=width\\ H=height\\ ------\\ L=6\\ W=4\\ H=10 \end{cases}\implies V=6\cdot 4\cdot 10\implies V=240\\\\ -------------------------------\\\\ \begin{cases} L=6(2)\\ W=4(2)\\ H=10(2) \end{cases}\implies V=6(2)8(2)10(2)\implies V=(2)(2)(2)6\cdot 8\cdot 10 \\\\\\ V=(8)6\cdot 8\cdot 10\implies V=(8)\stackrel{original~volume}{240}$

notice, how many times the new size is, is 8 times the original.