http://i207.photobucket.com/albums/b...EvErSe_/22.jpg
I have absolutely no idea how to do this or even start it
http://i207.photobucket.com/albums/b...EvErSe_/22.jpg
I have absolutely no idea how to do this or even start it
Let k be the amount of light admitted per unit area of glass.
The total amount of light admitted by the whole window is:
$\displaystyle L=k(\text{area of clear glass})+\frac{1}{2}k(\text{area of colored glass})=2krh+\frac{1}{4}{\pi}kr^{2}$
But the perimeter is $\displaystyle P=2h+2r+{\pi}r$
$\displaystyle h=\frac{1}{2}(P-2r-{\pi}r)$
So,
$\displaystyle L=kr(P-2r-{\pi}r)+\frac{1}{4}{\pi}kr^{2}=k\left[Pr-(2+{\pi}-\frac{\pi}{4})r^{2}\right]=k\left[Pr-\frac{8+3\pi}{4}r^{2}\right]$
for $\displaystyle 0<r<\frac{P}{2+{\pi}}$
Now, differentiate wrt r, set to 0 and solve for r.