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

AI Thread Summary
Uncertainties in measurements significantly impact calculations for cookie volume and size ratios. To find the average volume, the extreme values of diameter and thickness should be used to determine the range of possible volumes. For the diameter-to-thickness ratio, careful consideration is needed to avoid simply maximizing or minimizing all values simultaneously. The calculated average volume is 2.8 cm with an uncertainty of ±0.3 cm, while the diameter-to-thickness ratio is 170 with an uncertainty of ±20 cm. Understanding these uncertainties is crucial for accurate calculations in practical scenarios.
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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.
 
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iampaul said:

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
 

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