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

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) (Show Source): You can put this solution on YOUR website!
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 =
Find the area of the circle
A =
A =
A = sq/cm, the area of the circle
:
Find the area of the square
A = sq/cm the area of the square
The total area
At = +
Graph this equation, find the min

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