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The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?

 Apr 9, 2021
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Since area is \(A=\pi r^2\)  then  \(\frac{dA}{dt} = 2\pi r\frac{dr}{dt}\)

 

So the rate of change of area is \(2\pi r\) times the rate of change of radius.

 

I'll leave you to plug in the numbers.

 Apr 9, 2021

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