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.

Algebra ->  Surface-area -> 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.       Log On


   

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) About Me  (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 2pi%2Ax%29 = circumference of the circle
then
%2865-%282%2Api%2Ax%29%29 = perimeter of the square
:
%2865-%282%2Api%2Ax%29%29%2F4 = one side of the square
and
%28%2865-%282%2Api%2Ax%29%29%2F4%29%5E2 = the area of the square
Find the area of the circle
a = pi%2Ax%5E2
Find the total area
A = %28%2865-%282%2Api%2Ax%29%29%2F4%29%5E2 + pi%2Ax%5E2
Graphically

minimum area occurs when x = 4.55
C = 2%2Api%2A4.55
C = 28.6 is the circumference with minimum area