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# At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?

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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