Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · hard
A wire 100 cm long is cut into two pieces. One piece is bent into a square and the other into a circle. How many centimeters of wire should be used for the square so that the total enclosed area is a minimum?
- 56.01 cm
- 43.99 cm
- 50.00 cm
- 62.5 cm
Answer
A. 56.01 cm
Solution
Let x = length used for the square. Area =≤ft(x/4 )2+(100-x)2/4π. Setting the derivative to 0: x/8=100-x/2π x(2π+8)=800 x=800/2π+8 56.01 cm.
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