SOLUTION: Estimate the instantaneous rate of change in the area of a circle when the radius is 3 cm. The formula for the area of a circle is A=πr^2

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Question 1203952: Estimate the instantaneous rate of change in the area of a circle when the radius is 3 cm. The formula for the area of a circle is A=πr^2
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The area of a circle with respect to its radius can be modeled using the following function:
A%28r%29+=+pi%2Ar%5E2
The derivative of this function is as follows:
A '+%28r%29+=+2pi%2Ar

Therefore, the instantaneous rate of change of the area of a circle when the radius is 3+centimeters can be found by calculating A ' %283%29.

A ' %283%29+=+2pi%283%29+=+6pi+≈ 18.85
We get that the instantaneous rate of change of the area of a circle when the radius is 3+centimeters is approximately 18.85 area square centimeters per radius centimeter.


Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.
Estimate the instantaneous rate of change in the area of a circle
when the radius is 3 cm. The formula for the area of a circle is A=πr^2
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The problem is posed incorrectly. 

The formula for the instantaneous rate of change the area of a circle is

    %28dA%29%2F%28dt%29 = 2πr*r'(t),

where r(t) is the current radius of the circle as a function of t.

In order for the problem could be solved, the instantaneous rate r'(t) should be given
or should be calculated from other given data, but such data are missed in the problem.

The "solution" by the other person is INCORRECT and is an example of incorrect teaching.

For safety of your mind, simply ignore that "solution" as if you never seen it.