4s + 2πr = 47
A = s^2 + πr^2
since s = (47 - 2πr)/4 that means
A = ((47 - 2πr)/4)^2 + πr^2
dA/dr = π/4 ((8+2π)r - 47)
minmum area is when dA/dr = 0, so that gives
r = 47/(8+2π)
and the circumference is 47π/(4+π)
You have a wire that is 47 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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