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?
l=50 m±1 cm, d=1 mm±0.5μm,l=50~m±1~cm,~d=1~mm±0.5\mu m,l=50 m±1 cm, d=1 mm±0.5μm,
V±ΔV=π4(d2l±(2dlΔd+d2Δl))=π4(10−6⋅50±(2⋅10−3⋅50⋅0.5⋅10−6+10−6⋅0.01))=π4⋅10−6⋅(50±0.06) m3=π4⋅(50±0.06) cm3.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.V±ΔV=4π(d2l±(2dlΔd+d2Δl))=4π(10−6⋅50±(2⋅10−3⋅50⋅0.5⋅10−6+10−6⋅0.01))=4π⋅10−6⋅(50±0.06) m3=4π⋅(50±0.06) cm3.
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