SOLUTION: You have a wire that is 65 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.

Question 842373: You have a wire that is 65 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 minium?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
You have a wire that is 65 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?
:
perimeter + circumference = 65
let = circumference of the circle
then
= perimeter of the square
:
= one side of the square
and
= the area of the square
Find the area of the circle
a =
Find the total area
A = +
Graphically

minimum area occurs when x = 4.55
C =
C = 28.6 is the circumference with minimum area

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