Posted by **jin** on Saturday, August 28, 2010 at 1:25am.

The circumference of a sphere was measured to be 78.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area.

Estimate the relative error in the calculated surface area.

- calculus -
**drwls**, Saturday, August 28, 2010 at 9:05am
The relative error in area is, to first approximation, twice the relative error in a linear dimension.

That is because

(delta A)/A = (1 + epsilon)^2 - 1

= 1 + 2 epsilon + epsilon^2 - 1

= 2 epsilon

when epsilon << 1

In your case, the answer is

2*0.5/78 = 1/78 = 1.3%

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