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!
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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!
Hint: $\displaystyle \displaystyle \begin{align*} \frac{dA}{dr} \approx \frac{\Delta A}{\Delta r} \implies \Delta A \approx \Delta r \, \frac{dA}{dr} \end{align*}$.
I tried to solve it with your hint but still can't.. mind giving me the full solution?
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.
(delta)A = dA/dr x (delta)r = 2*Pi*r*0.05 = 10 x 0.05 = 0.5 cm^2
Is it correct?
Is it your radius which has changed by 0.05cm?
So the change in r = 0.05/(2*Pi) ?
