Question

A box has length 6 feet, width 3 feet, and height 7 inches. Find the volume of the box in cubic feet and in cubic inches. _____cubic inches _____cubic feet

Answer 1

We need to find the volume of the given box in cubic inches and in cubic feet.

In order to do so, we can use the conversion:

$1ft=12in$

Thus, we have:

$\begin{gathered} 6ft=6\cdot12in=72in \\ \\ 3ft=3\cdot12in=36in \\ \\ 7in=7\cdot\frac{1ft}{12}=\frac{7}{12}ft \end{gathered}$

Thus, using the same units for the dimensions of the box, its volume V is:

$V=72in\cdot36in\cdot7in=(72\cdot36\cdot7)in^3=18144in^3$

Also:

$V=6ft\cdot3ft\cdot\frac{7}{12}ft=(6\cdot3\cdot\frac{7}{12})ft^{3}=10.5ft^{3}$

Therefore, the volume can be written as:

$\begin{gathered} 18144\text{ cubic inches} \\ \\ 10.5\text{ cubic feet} \end{gathered}$