SOLUTION: A 24 cm piece of string is cut into two pieces , one piece is used to form a circle and the other piece is used to form a square. How should this string be cut so that the sum of t

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Question 825646: A 24 cm piece of string is cut into two pieces , one piece is used to form a circle and the other piece is used to form a square. How should this string be cut so that the sum of the areas is a minimum .
Thanks so much in advance:)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A 24 cm piece of string is cut into two pieces , one piece is used to form a circle and the other piece is used to form a square.
How should this string be cut so that the sum of the areas is a minimum .
:
Let x = the circumference of the circle
then
(24-x) = the perimeter of the square
:
Find the area of the circle
find r
2*pi*r = x
r = x%2F%282%2Api%29
Find the area of the circle
A = pi%2A%28x%2F%282%2Api%29%29%5E2
A = pi%2A%28x%5E2%2F%284%2Api%5E2%29%29
A = %28x%5E2%2F%284%2Api%29%29 sq/cm, the area of the circle
:
Find the area of the square
A = %28%2824-x%29%2F4%29%5E2 sq/cm the area of the square
The total area
At = %28%2824-x%29%2F4%29%5E2 + %28x%5E2%2F%284%2Api%29%29
Graph this equation, find the min

Min occurs when x=10.6 cm
cut string 10.6 cm from one end