If the length, width, and height of the box are $x\,y$, and $z$ respectively, the volume of the box is given by the function $f\left(x\,y\,z\right)\=x y z$. The interior volume is approximately $9\times 7\times 5\=315$ plus the "error" given by the differential

By this calculation, the interior volume is approximately $315-214.5\=100.5$.

However, the interior volume is given exactly by

 $\left(9-3\/2\right)\cdot \left(7-3\/2\right)\cdot \left(5-3\/2\right)$ = $\frac{1155}{8}$$\doteq$$144.38$