a Find the average volume of the disk and the uncertainty of

a) Find the average volume of the disk and the uncertainty of the volume.

Solution

consider the circular to be cylinder of volume pi*(t+ u1)((r+u2)^2)

t = thickness
r = radius
u1 = measured deviation from standard radius
u2 = measured deviation from standard thickness
m1 = maximum uncertainty of radius
m2 = maximum uncertainty of thickness

the average volume of the cookie for independent errors is

pi*average r * average r * average thickness

the uncertainty is largest cookie - smallest cookie

pi*(t+ m1)((r+m2)^2) - pi*(t - m1)((r-m2)^2)

b)

(2r+u2)/(t+u1)

uncertainty is largest numerator/smallest denominator - smallest numerator/largest denominator

(2r+m2)/(t-m1) - (2r-m2)/(t+m1)

substitute appropriate values and calculate