A piece of wire 10 feet long is cut into two pieces. One piece is bent into the shape of a circle and the other into the shape of the square. How should the wire be cut so that the combined area of the two figures is as small as possible?
3 answers
i'm sorry, this is about optimization problems.
x and (10 - x)
x is 2 pi r
r = x/(2 pi)
Ac = pi r^2 = pi x^2/(4pi^2) = x^2/(4pi)
(10 -x) = 4*side = 4 s
so
s = (10-x)/4
As = s^2 = (100-20 x + x^2)/16
A= Ac+As = x^2/4pi + (1/16)(x^2-20x+100)
dA/dx = 0 for max or min
0= x/2pi +1/16 (2x-20)
0= .16 x + .125 x - 1.25
0= .285 x - 1.25
x = 4.4
x is 2 pi r
r = x/(2 pi)
Ac = pi r^2 = pi x^2/(4pi^2) = x^2/(4pi)
(10 -x) = 4*side = 4 s
so
s = (10-x)/4
As = s^2 = (100-20 x + x^2)/16
A= Ac+As = x^2/4pi + (1/16)(x^2-20x+100)
dA/dx = 0 for max or min
0= x/2pi +1/16 (2x-20)
0= .16 x + .125 x - 1.25
0= .285 x - 1.25
x = 4.4
5inches