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.


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}