Question

A length of copper wire was measured with a tape measure to give a length of 50.0m with an uncertainty of 1 cm. The thickness of the wire was measured to be 1.00mm,using a micrometer screw gauge. Calculate the volume of the copper used?

Answer 1

$l=50~m±1~cm,~d=1~mm±0.5\mu m,$

$V±\Delta V=\frac{\pi}{4}(d^2l±(2dl\Delta d+d^2 \Delta l))=\frac{\pi}{4}(10^{-6}\cdot 50±(2\cdot 10^{-3}\cdot 50\cdot 0.5\cdot 10^{-6}+10^{-6}\cdot 0.01))=\frac{\pi}{4}\cdot 10^{-6}\cdot (50±0.06)~m^3=\frac{\pi}{4}\cdot (50±0.06)~cm^3.$