Question
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?
Answers
:)
i'm sorry, this is about optimization problems.
Damon
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
Kassahun
5inches