How Do Uncertainties Affect Calculations in Cookie Volume and Size Ratios?

[iampaul]

Homework Statement

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+-0.02cm and a thickness of 0.050+-0.005cm.

Homework Equations

a. Find the average volume of of a cookie and the uncertainty in the volume.
b.Find the ratio of the diameter to the thickness and the uncertainty in the ratio.

The Attempt at a Solution

The answer for a is 2.8+-0.3cm
The answer for b is 170+-20cm
Can someone please show how . Thanks.

 

[PeterO]

Homework Statement

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+-0.02cm and a thickness of 0.050+-0.005cm.

Homework Equations

a. Find the average volume of of a cookie and the uncertainty in the volume.
b.Find the ratio of the diameter to the thickness and the uncertainty in the ratio.

The Attempt at a Solution

The answer for a is 2.8+-0.3cm
The answer for b is 170+-20cm
Can someone please show how . Thanks.

(a) One way is to use extreme values of diameter and thickness, as well as the middle value to get the middle value and extremes of volume, then see what range is needed to cover the answers.

ie for mean: d= 8.50, th = 0.050

Upper d = 8.52 th = 0.055

Lower d = 8.48 th = 0.450

(b) you can sort of do the same thing, but must be careful that you don't alwys get the upper limit by making all values as big as possible, and similarly smallest doesn't mean all small. [this time you are using the d:th ratio of course. In part (a) you finding the volume