I am asked to solve the following problem:

Using differentials find the approximate decrease on the area of a circle when the radius of it decreases from $r = 1 cm$ to $r = 0.8 cm$

What I have so far is

$$ r' = -0.2 cm\\ \\ A' = 2 \pi r \cdot r'\\ A' = 2 \pi \cdot 1 \cdot (-0.2)\\ A' = -0.4 \pi cm^2 $$

Is that correct? Am I missing something here?

Thank you.


I would use primes for derivatives and $\Delta$ for changes, so $A'=2\pi r, \Delta A = 2 \pi r \Delta r$ and so on. The answer and approach are fine.

  • $\begingroup$ I understand, thank you. $\endgroup$ – bru1987 May 28 '16 at 22:52

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