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

Click For Summary
SUMMARY

The discussion focuses on calculating the average volume and size ratios of chocolate chip cookies, specifically a circular disk with a diameter of 8.50±0.02 cm and a thickness of 0.050±0.005 cm. The calculated average volume is 2.8±0.3 cm³, while the diameter-to-thickness ratio is 170±20. The methodology involves using extreme values for diameter and thickness to determine the range of volume and ratio uncertainties, ensuring accurate calculations by considering both upper and lower limits.

PREREQUISITES
  • Understanding of basic geometry, specifically circular disks
  • Familiarity with volume calculation formulas for cylinders
  • Knowledge of uncertainty propagation in measurements
  • Ability to perform ratio calculations and analyze their uncertainties
NEXT STEPS
  • Study the formula for the volume of a cylinder and its application in real-world scenarios
  • Learn about uncertainty propagation techniques in experimental physics
  • Explore methods for calculating ratios and their uncertainties in measurements
  • Investigate the impact of measurement precision on scientific calculations
USEFUL FOR

This discussion is beneficial for students in physics or engineering, particularly those working on measurement and uncertainty analysis, as well as educators teaching concepts related to geometry and volume calculations.

iampaul
Messages
93
Reaction score
0

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.
 
Physics news on Phys.org
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
 

Similar threads

Replies
9
Views
10K
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
12
Views
29K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
5
Views
4K
Replies
18
Views
9K
Replies
2
Views
3K
Replies
7
Views
6K