Homework Help: Related rates

Posted by :) on Sunday, May 20, 2012 at 9:02pm.

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?

Related rates - :), Sunday, May 20, 2012 at 9:03pm
i'm sorry, this is about optimization problems.
Related rates - Damon, Sunday, May 20, 2012 at 9:34pm
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

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