As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 ± 0.02 cm and a thickness of 0.050 ± 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio of the diameter to the thickness and the uncertainty in this ratio.
d=8.50 +/- 0.02 cm → r=4.25+-0.01 cm
The Attempt at a Solution
a.) average volume V=pi*r^2*h=pi*(4.25cm)2*0.050cm≈2.8cm3
volume of the smallest cookie V=pi*(4.24cm)2*0.045cm=2.54152...cm3
volume of the biggest cookie V=pi*(4.26cm)2*0.055cm=3.1356...cm3
uncertainty= (biggest - smallest)/2=0.30cm3
b.) ratio of the diameter to the thickness= 8.50cm/0.050cm=170
uncertainty=biggest ratio-smallest ratio=8.52cm/0.045cm-8.48cm/0.055cm=35
Please check my answers. I am not sure what is meant with that uncertainty thing.