Example 5. How will the volume of a rectangular parallelepiped with dimensions $a=8 \, m, b=6 \, m, c=3 \, m$ change when its length and width
increase by $10 \, \mathrm{cm}$ and $5 \, \mathrm{cm}$ respectively, and its height decreases by $15 \, \mathrm{cm}$.
Solution. The volume of a parallelepiped is expressed by the formula $V=x y z$, where $x, y, z,$ are its dimensions. The increment of volume can be approximately calculated by the formula

$$
\Delta V \approx d V, \text { where } d V=y z d x+x z d y+x y d z
$$

Since according to the condition $x=8, y=6, z=3, d x=0.1, d y=0.05, d z=-0.15$, then

$$
d V=6 \cdot 3 \cdot 0.1+8 \cdot 3 \cdot 0.05+8 \cdot 6 \cdot(-0.15)=1.8+1.2-7.2=-4.2
$$

Thus, the volume will decrease by $4.2 \mathrm{M}^{3}$.