Question #171173

) A metal cylinder has a length of 4 cm and diameter 2 cm. What percent uncertainty is introduced into the calculated circumference by an uncertainty of 0.01 cm in the diameter measurement? What percent uncertainty does this introduce in the calculated volume?


1
Expert's answer
2021-03-14T19:14:30-0400

Given,

Length of the metal cylinder (l)=4cm(l)=4cm

Diameter (d)=2cm(d)=2cm

Uncertainty in the measurement of circumference = 0.01cm

percentage uncertainty in the measurement of volume(V)=?

ΔVV×100=2Δrr×100+Δll×100\frac{\Delta V}{V}\times 100 =\frac{2\Delta r}{r}\times 100 + \frac{\Delta l}{l}\times 100


=0.01×2×1001+4×0.01×1004=\frac{0.01\times 2\times 100}{1}+\frac{4\times 0.01\times 100}{4}

=2+1=3%=2+1 = 3\%

Hence, the required change in volume be 3%.


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