A cylindrical tank has radius with uncertainty ( per cent

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Propagating uncertainty into the quantity you actually want

Problem

A cylindrical tank has radius r=0.500 mr = 0.500\,\mathrm{m} with uncertainty u(r)=0.002 mu(r) = 0.002\,\mathrm{m} (0.400.40 per cent, one standard deviation) and height h=1.200 mh = 1.200\,\mathrm{m} with uncertainty u(h)=0.006 mu(h) = 0.006\,\mathrm{m} (0.500.50 per cent, one standard deviation), the two measured independently. The volume is V=πr2hV = \pi r^2 h. Find the error(s) in the following working and give a corrected result."u(V)V=2(0.40%)+0.50%=1.30%\dfrac{u(V)}{V} = 2(0.40\%) + 0.50\% = 1.30\%. V=π(0.500)2(1.200)=0.9425 m3V = \pi(0.500)^2(1.200) = 0.9425\,\mathrm{m^3}. u(V)=1.30%×0.9425 m3=0.012251 m3u(V) = 1.30\%\times0.9425\,\mathrm{m^3} = 0.012251\,\mathrm{m^3}. So V=(0.942506±0.012251) m3V = (0.942506 \pm 0.012251)\,\mathrm{m^3}."

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