College Physics Problem 1.28

A car engine moves a piston with a circular cross section of  7.500±0.002 cm diameter a distance of 3.250±0.001 cm  to compress the gas in the cylinder.
(a) By what amount is the gas decreased in volume in cubic centimeters?
(b) Find the uncertainty in this volume.

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The average volume is

V=pi r^{2}h

V=pi left (frac{7.5 cm}{2}right )^{2}left (3.25 cmright )

V=143.5806 cm^{3}

Get the percent uncertainties for the dimensions

% unc_{r}=frac{0.002 cm}{7.500 cm}times 100%=0.027%

% unc_{h}=frac{0.001}{3.25}times 100%=0.031%

The percent uncertainty in the volume is the combined effect of the uncertainties of the dimensions

% unc_{vol}=0.027% + 0.031%

% unc_{vol}=0.058%

The uncertainty in the volume is

delta_{vol}=frac{0.058}{100}times 143.5806 cm^{3}

delta_{vol}=0.083 cm^{3}

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