What is the approximate uncertainty in the area of a circle

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SUMMARY

The approximate uncertainty in the area of a circle with a radius of 5.5×104 cm is calculated using the formula A = πr2. Given the radius is expressed to two significant figures, the uncertainty in the radius is ±0.05×104 cm, translating to ±500 cm. This results in a possible radius range of 5.45×104 cm to 5.55×104 cm, which leads to an area uncertainty that must be calculated based on these radius limits.

PREREQUISITES
  • Understanding of the formula for the area of a circle (A = πr2)
  • Knowledge of significant figures and their implications in measurements
  • Basic grasp of uncertainty in measurements
  • Familiarity with the concept of range in mathematical contexts
NEXT STEPS
  • Calculate the area of a circle using the given radius and its uncertainty
  • Explore the concept of propagation of uncertainty in calculations
  • Learn about significant figures and their importance in scientific measurements
  • Investigate how to report uncertainties in scientific contexts
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Students studying mathematics or physics, educators teaching measurement concepts, and anyone interested in understanding uncertainty in geometric calculations.

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Homework Statement


Approximate uncertainty in the area of a circle of radius 5.5×10^4 cm?


Homework Equations


πr^2



The Attempt at a Solution

 
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What are the smallest and largest possible values for the radius? What are the smallest and largest possible values for the area?
 
It doesn't say. That's all the information it gives. That's why I was confused.
 
Well if the radius is stated to two significant figure as 5.5×10^4cm then the uncertainty is ±0.05x104cm (or ±500cm) and the possible range is 5.45x104cm to 5.55x104cm.
 
People, please report members that do not fill out the template, it is against our rules for members to request help without completing the entire template, especially the part explaining what they've already done to soleve the problems themselves.
 
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