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I could use some help with this question; it was taught a few weeks ago in Calculus class, but I was out sick that day (so I ended up getting the question wrong on my make-up homework). I was hoping you could briefly explain the problem and the answer.

The radius of a circle is increasing at a constant rate of 10 meters per second. What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 100*pi meters?

Thanks,

Clark

It is known that the area of a circle is A = pi*rē.

This is an equation for A in terms of r.

Taking the derivative gives A' = 2rr'.

If the circumference is 100*pi, the radius can be found.

Since 2*pi*r = c, we have r = c/(2*pi).

That is, r = 100*pi/(2*pi), so r = 50.

Since r = 50 and r' = 10, A' = 2*50*10 = 1,000.

By the way, the units are in mē/2.

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