Posted by John on Friday, February 19, 2010 at 12:09am.
The circumference of a sphere was measured to be 88000 cm with a possible error of 050000 cm. Use linear approximation to estimate the maximum error in the calculated surface area.
Estimate the relative error in the calculated surface area.

Calculus  John, Friday, February 19, 2010 at 12:15am
Oops the 88000 is supposed to be 88 cm and 0.5 cm

Calculus  MathMate, Friday, February 19, 2010 at 7:55am
Circumference, C=88 cm
C = 2πr
Area, A=πr²
Differentiating:
dA/dr = 2πr
Using linear approximation:
δA = 2πr δr
=2πr δr
=C δr
=88 cm * 0.5 cm
=44 cm²
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