Let the square have side s, and the circle have radius r. Then
4s+2πr = 83
A = s^2 + πr^2 = ((83-2πr)/4)^2 + πr^2
you will find that A is a minimum where dA/dr = 0, at r = 83/(2π+8)
You have a wire that is 83 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?
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