Rate of change of area of circle in respect to radius

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Discussion Overview

The discussion revolves around the rate of change of the area of a circle with respect to its radius, specifically when the radius is 3 inches. Participants explore the relationship between the area and circumference, as well as the units involved in this context.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant inquires about the rate of change of area with respect to radius, noting that dA/dr equals the circumference of the circle and seeks clarification on this relationship.
  • Another participant emphasizes the need to understand the units of area and radius in this context.
  • A different participant suggests that the formula for circumference can be used, but questions how the units for area and radius interact in this calculation.
  • Some participants assert that the concepts of area and circumference are fundamentally linked in this discussion, but express that using appropriate units for rate of change is important.
  • One participant reminds others that homework questions should be directed to the appropriate forums.

Areas of Agreement / Disagreement

Participants generally agree on the relationship between the area and circumference in terms of rate of change, but there is some confusion regarding the units involved and how they should be represented. The discussion remains unresolved regarding the clarity of these units.

Contextual Notes

There are limitations in the discussion regarding the assumptions about units and the mathematical steps involved in deriving the rate of change, which have not been fully resolved.

grace77
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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.
 
Homework questions need to be posted in the homework forums.
 

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