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If you mean average rate of area increase, it is 4pi cm2/cm. Simply take the total change in area, 9pi-1pi=8pi, and divide it by the total expansion.

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Q: What is the average rate of increase of the circle when the radius is from 1 cm to 3 cm?
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The area of a circle is increasing at a uniform rate of 8cm square per second Calculate the rate of increase of the radius when the circumference of the circle is 96cm?

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