A car engine moves a piston with a circular cross section of 7.500 ± 0.005cm 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.
Area = πr2
ΔVolume = Area × ΔDistance
%unc = (ΔA/A) × 100%
The Attempt at a Solution
The radius of the cross section of the piston is 3.75cm so the area comes out to 44.18 cm2
The change in volume then comes out to 143.6cm3
-This value is measured to 4 significant figures because both the diameter and the distance were given to 4 significant figures.The percent uncertainty in the diameter comes out to 0.0267%
The percent uncertainty in the distance comes out to 0.0308%
The percent uncertainty in the change in volume should then be these values added together, giving 0.0575%
-With the correct number of significant figures this should be 0.06% because the original uncertainties (0.005 and 0.001) both had only 1 significant figure.Then, to get the uncertainty for the change in volume you use %unc = (ΔA/A) × 100% and solve for ΔA
-For this I got 0.08618 which comes to ± 0.09cm3
My question is: If the change in volume (143.6cm3) has the correct number of significant figures but is measured only to the nearest tenth of a centimeter, then how can the uncertainty (±0.09cm3) be in hundredths of a centimeter?