# Thread: Error calculation using differential

1. ## Error calculation using differential

The circumference of a sphere was measured to be 10 cm with a possible error
of 0.05 cm. Use diﬀerentials to estimate the maximum error in the calculated
surface area. Thanks!

2. ## Re: Error calculation using differential

Hint: \displaystyle \displaystyle \begin{align*} \frac{dA}{dr} \approx \frac{\Delta A}{\Delta r} \implies \Delta A \approx \Delta r \, \frac{dA}{dr} \end{align*}.

3. ## Re: Error calculation using differential

I tried to solve it with your hint but still can't.. mind giving me the full solution?

4. ## Re: Error calculation using differential

Yes I do mind in fact. The expectation is that students do their own work, and the rules of this site are that if you ask a question, you are supposed to attempt it yourself, show what you have tried (so show all your working out) and exactly where you are stuck. Then we can give you more specific guidance.

5. ## Re: Error calculation using differential

(delta)A = dA/dr x (delta)r = 2*Pi*r*0.05 = 10 x 0.05 = 0.5 cm^2
Is it correct?