Hi

Can someone tell me why my answer is incorrect.

The area of the circle segment is given by

$\displaystyle A=\frac{1}{2}r^2(\theta - sin(\theta)$

The radius r is measured with a maximum percentage error of 0.2% and $\displaystyle \theta$ (the angle subtended at the circle's center) is measured as 45 degrees with a maximum error of 0.1 degrees. Find the approximately the maximum percentage error in the calculated area.

This is my attempt on the question:

$\displaystyle \partial r = \frac{0.2r}{100}$

$\displaystyle \partial \theta = \frac{0.1\pi}{180}$

$\displaystyle \frac{\partial A}{\partial r} = r\theta-rsin(\theta}$

$\displaystyle \frac{\partial A}{\partial r} = \frac{1}{2}r^2-\frac{1}{2}r^2cos(\theta)$

$\displaystyle \partial A = [r(\theta-sin(\theta)](\frac{0.2r}{180})+[\frac{1}{2}r^2(1-cos(\theta)](\frac{0.1\pi}{180})$

$\displaystyle \partial A = [r(\frac{45\pi}{180}-sin(\frac{45\pi}{180})](\frac{0.2r}{180})+[\frac{1}{2}r^2(1-cos(\frac{45\pi}{180})](\frac{0.1\pi}{180})$

$\displaystyle

\partial A =[\frac{\pir^2}{3600}-\frac{sin(\frac{\pi}{4}}{900}]+[\frac{\pir^2}{3600}-\frac{\pir^2}{3600}cos(\frac{\pi}{4}]$

$\displaystyle

\partial A = 3.425879759*10^-4$

$\displaystyle A = \frac{1}{2}r^2(\frac{45\pi}{180}-sin(\frac{45\pi}{180}))$

A = 0.0391456911

Maximum error is $\displaystyle \frac{3.425879759*10^-4}{0.0391456911} * 100 = 0.88% $

P.S