Homework Help: Math

Posted by ME on Sunday, August 8, 2010 at 5:32pm.

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?

Math - Damon, Sunday, August 8, 2010 at 6:40pm
square
side = s, area = s^2
circle
circumference = c, area = pi d^2/4 = c^2/(4pi)

4s + c = 35 so c = (35-4s)
a = s^2 + c^2/(4pi)
a = s^2 + (35-4s)^2/(4pi)
a = s^2 + (1225-280s+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 = 35-4*4.91 = 15.3

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