Rate of change of area of circle in respect to radius

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SUMMARY

The rate of change of the area of a circle with respect to its radius is defined as dA/dr, which equals the circumference of the circle, expressed mathematically as 2πr. For a radius of 3 inches, this results in a rate of change of 6π in²/in. The units of this expression arise from the relationship between area and radius, where the area is measured in square inches and the radius in inches, leading to the derived units of in²/in. Understanding this relationship clarifies the dimensional analysis involved in calculus.

PREREQUISITES
  • Understanding of basic calculus concepts, specifically derivatives.
  • Familiarity with the formula for the area of a circle: A = πr².
  • Knowledge of the formula for the circumference of a circle: C = 2πr.
  • Basic understanding of dimensional analysis in physics and mathematics.
NEXT STEPS
  • Study the concept of derivatives in calculus, focusing on geometric applications.
  • Explore the relationship between area and circumference in circles through practical examples.
  • Learn about dimensional analysis and its importance in physics and engineering.
  • Investigate related topics such as the rate of change in other geometric shapes.
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in the geometric properties of circles and their applications in real-world scenarios.

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What is the Rate of change of area of circle in respect to radius when radius is 3in
I know that that dA/dr is equal to the circumference of the circle
But where does that come from?
Also the formula for the circumference of the circle is 2(pi)r
But the answer is 6 (pi)in^2/in.
I understand the 6 but where are the units coming from if the circumference of the circle will only give you units for r ?

Hope someone can shed some light on this for me! Thanks
 
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It is rate of change of AREA wrt RADIUS. What are the units of these two?
 
PhysicoRaj said:
It is rate of change of AREA wrt RADIUS. What are the units of these two?
Ok so you basically use the formula for the circumference of the circle but use the units for area/radius?
 
Both are one and the same. But since we are representing the rate of change, it is better to use units like that.
 
PhysicoRaj said:
Both are one and the same. But since we are representing the rate of change, it is better to use units like that.
Thank you.
 
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