The area A of a circle is related to its radius by the equation A=πr2. The change in area with respect to the radius is x×πm. When the radius is 5m, find the value of x.
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Solution
The (instantaneous) rate of change of the area with respect to the radius is dAdr=2πr
When r=5m,
the area is changing at the rate of =(π)10=10πm2/m