As you eat ur way through a bag of cookies, you observe each cookie is a circular disk of diamter 8.50+ or - 0.02 cm and thickness 0.050+ or - 0.005cm. Find the avg volume of a cookie and the uncertainty in the volume.

Answer 1

The average volume is (pi/4) D^2 T, where D and T are the mean diameter and thickness.

Assuming the variations in D and T are uncorrelated, the relative uncertainty in volume is

ln V = ln (constant*D^2*T)

dV/V = sqrt[(2 dD/D)^2 + (dT/T)^2]
= sqrt [(.005)^2 + (0.1)^2]
= 0.1

The volume uncertainty is almost entirely due to the thickness variation.