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!

Printable View

- Jun 8th 2013, 12:30 AMyugimutoshungError 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! - Jun 8th 2013, 12:53 AMProve ItRe: Error calculation using differential
Hint: $\displaystyle \displaystyle \begin{align*} \frac{dA}{dr} \approx \frac{\Delta A}{\Delta r} \implies \Delta A \approx \Delta r \, \frac{dA}{dr} \end{align*}$.

- Jun 8th 2013, 12:55 AMyugimutoshungRe: Error calculation using differential
I tried to solve it with your hint but still can't.. mind giving me the full solution?

- Jun 8th 2013, 12:57 AMProve ItRe: 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.

- Jun 8th 2013, 01:10 AMyugimutoshungRe: 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? - Jun 8th 2013, 01:14 AMProve ItRe: Error calculation using differential
Is it your radius which has changed by 0.05cm?

- Jun 8th 2013, 01:24 AMyugimutoshungRe: Error calculation using differential
So the change in r = 0.05/(2*Pi) ?