Question

A car engine moves a piston with a circular cross section of 7.200 ± 0.009 cm diameter a distance of 3.190 ± 0.001 cm to compress the gas in the cylinder. (Express your answers to the correct number of significant figures.) (a) By what amount is the gas decreased in volume in cubic centimeters?

Answer 1

The decrease in volume of the cylinder, V =
`129.88 cm^(3)`

Given:

Diameter of the circular cross section, d = 7.20 ± 0.009

Distance moved by the piston, h = 3.190 ± 0.001

Solution:

Since the values are given with some percentage error in the format x±
`\Delta x`, so calculate the decrease in volume we consider the 'x' part of the values.

Now, the decrease in volume of cylinder is given by:

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

Therefore,

V =
`\pi* ((7.20)/(2))^(2)* 3.190 = 129.88 cm^(3)`