The area of a circle is related to its radius via the equation `A=pi*r^2` .Find the area of the circle w/ respect to its radius r as r changes from: (2 to 3), (2 to 2.5) and (2 to 2.1). Find the...

The area of a circle is related to its radius via the equation `A=pi*r^2` .

Find the area of the circle w/ respect to its radius r as r changes from: (2 to 3), (2 to 2.5) and (2 to 2.1). Find the instantaneous rate of change of area.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The area of a circle in terms of its radius r is `A = pi*r^2` .

The change in the value of the area of the circle when its radius changes is:

  • r changes from 2 to 3 : area changes from `pi*4` to `pi*9`
  • r changes from 2 to 2.5 : area changes from `pi*4` to `pi*6.25`
  • r changes from 2 to 2.1: area changes from `pi*4` to `pi*4.41`

The instantaneous rate of change of area with respect to radius is `(dA)/(dr) = 2*pi*r = pi*D`

The instantaneous rate of change of area is `pi*D`

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