SOLUTION: A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much of the wire should go to the square to maximi

Algebra ->  Length-and-distance -> SOLUTION: A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much of the wire should go to the square to maximi      Log On


   

Question 1141838: A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
(a) How much of the wire should go to the square to maximize the total area enclosed by both figures?

(b) How much of the wire should go to the square to minimize the total area enclosed by both figures?
I got 11.201m for this
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
A way to start is like this:
x, the amount to make the square
20-x, the amount to make the circle.

Area of Square: %28x%2F4%29%5E2=x%5E2%2F16

Area of Circle: circumference with radius r, 2pi%2Ar=20-x%7D%7D%0D%0Ameaning+%7B%7B%7Br=%2820-x%29%2F%282pi%29
--
Area of this part, %2820-x%29%5E2%2F%284pi%29

A, the total area of combined square and circle:
highlight_green%28A=x%5E2%2F16%2B%2820-x%29%5E2%2F%284pi%29%29
This function is what you want to find the minimum for.

The differentiation and algebraic steps should give
highlight_green%28dA%2Fdx=%28%288%2Bpi%29x-160%29%2F%288pi%29=0%29
and solving for x should be no trouble.