#### 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.

## Solution:

### Part a

The average volume is

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### Part b

Solve for the percent uncertainties of each dimension

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

The uncertainty in the volume is

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