As you eat your way through a bag of chocolate chip cookies, you observe that ea

Question

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 d = 10 cm +/- 1x10^(-2) cm and a thickness of of h = 4.0x10^(-2) cm +/- 5x10^(-4) cm.

Part A: Find the average volume of a cookie
Part B: Find the uncertainty in the volume of a cookie
Part C: Find the ratio of the diameter to the thickness
Part D: Find the uncertainty in this ratio

I found part A to be 3.14, part B to be 4.56x10^(-2), part C to be 250. I need help to solve for Part D please. Thank you!

Explanation / Answer

Percentage uncertainty in diameter d = 100*(10-2/10) = 0.1

Percentage uncertainty in thickness t = 100*(5*10-4/4*10-2) = 1.25

Percentage uncertainty in the ratio d/t = 0.1 + 1.25 = 1.35 %

Uncertainty in d/t = 1.35 * (10 / 4.0x10-2) *(1/100) = 3.375

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