SOLUTION: I have no idea where to start with this one... You have a wire that is 53 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The oth

Algebra ->  Rational-functions -> SOLUTION: I have no idea where to start with this one... You have a wire that is 53 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The oth      Log On


   

Question 744782: I have no idea where to start with this one...
You have a wire that is 53 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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You have a wire that is 53 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?
:
let r = the radius of the circle
let s = the side of the square
:
We know the perimeter of the square and the circumference = 53, therefore
4s + 2pi%2Ar = 53
therefore
4s = 53 - 2pi%2Ar
s = %2853-%282pi%2Ar%29%29%2F4
:
Total area
A = pi%2Ar%5E2 + s%5E2
:
Replace s with %2853-%282pi%2Ar%29%29%2F4
A = %28pi%2Ar%5E2%29+%28%2853-%282pi%2Ar%29%29%2F4%29%5E2
Find the minimum area by graphing this equation

Putting the same equation in my Ti83, minimum area occurs when r=3.71
therefore
C = 2%2Api%2A3.71
C = 23.3 cm, circumference of the circle for min area of the circle & square