Question

A car engine moves a piston with a circular cross section of 7.500±0.002cm diameter a distance of 3.250±0.001cm 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.

Answer 1

a)
`V=143.54 cm^3`

b)
`\delta V=0.24 cm^3`

Explanation:

We know that

Volume of cylinder is gibe as follows

`V=(\pi)/(4)d^2h`

Now by putting the values

`V=(\pi)/(4)* 7.5^2* 3.25`

`V=143.54 cm^3`

`V=(\pi)/(4)d^2h`

`V_(max)=(\pi)/(4){7.502}^2* 3.251 cm^3`

`V_(max)=143.701 cm^3`

`V_(min)=(\pi)/(4)\left({7.5-0.002}\right)^2*\left({3.25-0.001}\right) cm^3`

`V_(min)=143.459 cm^3`

So the uncertainty in the volume

`\delta V=143.701-143.459 cm^3`

`\delta V=0.24 cm^3`