Chapter 1, Problem 22P

The volume of a rectangular parallelepiped is given by V = xyz, If x = a ± Δa, y = b ± Δb, z = c ± Δc, show that

$\frac{\Delta V}{\bar{V}}\approx \frac{\Delta a}{\bar{a}}\text{ + }\frac{\Delta b}{\bar{b}}\text{ + }\frac{\Delta c}{\bar{c}}$

Use this result to determine the bilateral tolerance on the volume of a rectangular parallelepiped with dimensions

a = 1.500 ± 0.002 in

b = 1.875 ± 0.003 in

c = 3.000 ± 0.004 in