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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