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Math Help - How to find how fast the circumference of a concentric circle is changing?

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    How to find how fast the circumference of a concentric circle is changing?

    In this problem there are two varying concentrical circles with a constant area between at 9pi in^2. The area of the larger circle has a rate of change of 10pi in^2/sec. How fast is the circumference of the smaller circle changing when it has an area of 16pi in^2?
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  2. #2
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    Re: How to find how fast the circumference of a concentric circle is changing?

    Let R be the area of the larger circle and r the area of the smaller circle. Then the area between them is \pi R^2- \pi r^2= \pi(R^2- r^2)= 9\pi. Now differentiate both sides with respect to t and use the fact that \frac{dR}{dt}= 10\pi and \pi r^2= 16\pi. What is R at that time?
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