Math
posted by ME on .
You have a wire that is 35 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum?

square
side = s, area = s^2
circle
circumference = c, area = pi d^2/4 = c^2/(4pi)
4s + c = 35 so c = (354s)
a = s^2 + c^2/(4pi)
a = s^2 + (354s)^2/(4pi)
a = s^2 + (1225280s+16s^2)/12.56
a = 2.27s^2  22.3 s + 97.5
that is a parabola, find the vertex or use calculus (I used calculus)
0 = 4.54 s 22.3
s = 4.91
c = 354*4.91 = 15.3