Answer:
Step-by-step explanation:
Given
Possible dimension error is [tex]\pm 0.02 in.[/tex]
length of box [tex]L=8 in.[/tex]
Width [tex]W=5 in.[/tex]
height [tex]h=12 in.[/tex]
Volume V is given by
[tex]V=LWh[/tex]
[tex]dV=LWdh+LhdW+WhdL[/tex]
and it is given
[tex]dL=dW=dh=\pm 0.02\ in.[/tex]
since error always add therefore
[tex]dV=(8\times 5+5\times 12+8\times 12)\cdot 0.02[/tex]
[tex]dV=3.92 in.^3[/tex]
Propagated error is [tex]3.92 in.^3[/tex]
relative error[tex]=\frac{dV}{V}[/tex]
[tex]=\frac{3.92}{480}[/tex]
[tex]=0.00816[/tex]
[tex]=0.816 \%[/tex]