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A wire of total length 2 units is divided into two pieces. One piece is shaped into a square and the other into a circle. If the combined area of the square and the circle is as small as possible, then
- x = 2r
- 2x = r
- 2x = (π + 4)r
- (4 − π)x = πr
Correct answer: x = 2r
Solution
With 2x+pi*r=1 (square side x, circle radius r), minimizing x^2+pi*r^2 gives x=2/(pi+4) and r=1/(pi+4), hence x=2r.
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