Question

A 3m piece of wire is cut into two pieces and bent around to form a square and a circle. Find the size of the two lengths, that will make the total area of the square and circle a minimum

Answer 1

Wire used:
\[3=4y+2x\pi\]
Total Area:
\[y^2+x^2\pi=TA\]

Graph both of these functions, and decrease TA until there is no overlap between the top of the first function and the second.

http://fooplot.com/
(3-(pi*2*x))/4
sqrt(TA-(pi*x^2))

Decrease TA until the there is an infinitely small space between the bell curve and the line. At the place where they touch, there you have your circle radius ans square length to use.