Originally Posted by

**silvercats** Part circle(radius is "r" ) is made from a string.string's lenght is "L".so the part

circle's circumference is also "L".If part circle's area is "A",Find the angle of the part

circle when Area is maximum

,here what I did but never got the answer.what is wrong in this?

$\displaystyle L=\frac{x}{360}2\pi r + 2r$

$\displaystyle A=\frac{x}{360}\pi r^{2}$

$\displaystyle x=\frac{360L-720r}{2\pi r}$

$\displaystyle A=\frac{360L-720r}{r}\pi r^{2}$

$\displaystyle \frac{\mathrm{dA} }{\mathrm{d} r}=360\pi L-2\ast 720\pi r$

setting to zero for the maximum value

$\displaystyle 360L=720*2r$

$\displaystyle r=4/L$

now what? answer has to be r(L-2r)/2(as books says).