Volume and its error…
Volume, VV = 40′ × 20′ × 15′ = 12,000 ft3
Take partial derivatives… ∂V∂L=WH\frac{\partial V}{\partial L}=WH, ∂V∂W=LH\frac{\partial V}{\partial W}=LH, and ∂V∂H=LW\frac{\partial V}{\partial H}=LW.
Now, SV=(∂V∂LSL)2+(∂V∂WSW)2+(∂V∂HSH)2S_V=\sqrt{\left(\frac{\partial V}{\partial L}S_L\right)^2+\left(\frac{\partial V}{\partial W}S_W\right)^2+\left(\frac{\partial V}{\partial H}S_H\right)^2}. Now, only thing left to do is fill in the variables.
Which is =(WH)2(0.05)2+(LH)2(0.03)2+(LW)2(0.02)2=\sqrt{(WH)^2(0.05)^2+(LH)^2(0.03)^2+(LW)^2(0.02)^2};=((20⋅15)×0.05)2+((40⋅15)×0.03)2+((40⋅20)×0.02)2=\sqrt{((20\cdot15)\times0.05)^2+((40\cdot15)\times0.03)^2+((40\cdot20)\times0.02)^2}; =225+324+256=805=\sqrt{225+324+256}=\sqrt{805}= ± 28 ft3
Chris
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