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

Answer:

a)$V=143.54 cm^3$

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

Step-by-step explanation:

We know that

Volume of cylinder is gibe as follows

$V=\dfrac{\pi}{4}d^2h$

Now by putting the values

$V=\dfrac{\pi}{4}\times 7.5^2\times 3.25$

$V=143.54 cm^3$

$V=\dfrac{\pi}{4}d^2h$

$V_{max}=\dfrac{\pi}{4}{7.502}^2\times 3.251 cm^3$

$V_{max}=143.701 cm^3$

$V_{min}=\dfrac{\pi}{4}\left({7.5-0.002}\right)^2\times\left({3.25-0.001}\right) cm^3$

$V_{min}=143.459 cm^3$

So the uncertainty in the volume

 $\delta V=143.701-143.459 cm^3$

$\delta V=0.24 cm^3$