College Physics Problem 1.25

The sides of a small rectangular box are measured to be 1.80±0.01 cm, 2.05±0.02 cm, and 3.1±0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.

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The average volume of the box is

Vol=ltimes w times h

Vol=left(1.80 cm right)left(2.05 cm right) left(3.1 cm right)

Vol=11.4  cm^{3}

The percent uncertainty for each of the dimensions:

1.80 pm0.01cmri frac{0.01 cm}{1.80 cm} times 100 %=0.556 %

2.05 pm0.02cmri frac{0.02 cm}{2.05 cm} times 100 %=0.976 %

3.1 pm0.1cmri frac{0.1 cm}{3.1 cm} times 100 %=3.226 %

The percent uncertainty in the volume of the box is calculated by adding the percent uncertainties of the dimensions.

%uncertainty_{vol}=0.556 %  +  0.976 % +  3.226 %

%uncertainty_{vol}=4.758 %

The uncertainty of the volume is

delta_{vol}=0.04758  times 11.4 cm^{3}

delta_{vol}=0.54 cm^{3}

Therefore, the volume is

11.4 pm  0.54  cm^{3}

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