How Do You Calculate Uncertainty in the Volume of a Cylinder?

  • Thread starter Thread starter Necrosity
  • Start date Start date
  • Tags Tags
    Cylinder
Click For Summary
SUMMARY

The discussion focuses on calculating uncertainties in the volume of a cylinder based on measurements of diameter and length. The diameter of the copper rod is measured at 24.8 ± 0.5 mm, and the length at 135 ± 0.5 mm. The percentage uncertainties calculated are 0.20% for diameter, 0.37% for length, and 0.77% for volume. The absolute uncertainty in the volume calculation requires further clarification and detailed working out.

PREREQUISITES
  • Understanding of basic geometry, specifically cylinder volume calculation
  • Familiarity with uncertainty propagation in measurements
  • Knowledge of percentage calculations
  • Experience using vernier calipers and meter rules for measurement
NEXT STEPS
  • Learn about uncertainty propagation techniques in physics
  • Study the formula for calculating the volume of a cylinder, V = πr²l
  • Explore methods for calculating absolute uncertainty from percentage uncertainties
  • Review examples of uncertainty calculations in real-world applications
USEFUL FOR

Students in physics or engineering courses, educators teaching measurement and uncertainty, and anyone interested in precision measurement techniques.

Necrosity
Messages
1
Reaction score
0

Homework Statement


9.The diameter of a cylindrical piece of copper rod was measured at a 24.8 +/- 0.5mm with a vernier caliper. Its length was measured at 135 +/- 0.5mm with a meter rule.

a. Calculate the percentage uncertainty in the diameter.
b. Calculate the percentage uncertainty in the length
c. Calculate the percentage uncertainty in the volume of the cylinder.
d. Calculate the absolute uncertainty in the volume of the cylinder in mm^3

Homework Equations


%U = AU/Measurement (atleast that's how i do it)
V = Pi x r^2 x l
Thats all i know.


The Attempt at a Solution


I figured out:
A. %U = 0.20%
B. %U = 0.37%
C. %U of V = 0.77%

But I've got no idea about D. Needs to show full working out.
 
Physics news on Phys.org
Welcome to PF :smile:

Before doing D, I'll suggest re-doing A and C. Post back here, then I can help with D.

(B is correct, by the way.)
 

Similar threads

Adjustment of Significant Figures
  • · Replies 11 ·
Replies
11
Views
2K
Time Uncertainty Propagation - Stoke's Law & Average Time
  • · Replies 2 ·
Replies
2
Views
2K
Propagation of Uncertainty - Hollow Cylinder
  • · Replies 1 ·
Replies
1
Views
4K
Uncertainty/error of a volume is greater than the normal volume
  • · Replies 4 ·
Replies
4
Views
1K
SigFigs in Volume and Uncertainty?
  • · Replies 4 ·
Replies
4
Views
5K
Stability of a floating cylinder
  • · Replies 7 ·
Replies
7
Views
3K
What is the focal length of the lens?
  • · Replies 20 ·
Replies
20
Views
4K
What is the percentage uncertainty in V when L1-L2 is 30?
  • · Replies 4 ·
Replies
4
Views
2K
Write the density and its associated uncertainty of a cylinder
  • · Replies 1 ·
Replies
1
Views
4K
How Do You Calculate Uncertainty in the Volume of a Cookie?
  • · Replies 9 ·
Replies
9
Views
10K