Question

A piece of wire 8 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 wire should be used for the square in order to maximize the total area?
(b) How much wire should be used for the square in order to minimize the total area?

Answer 1

Solution to part A is 0, meaning all of the wire should be used for the circle to maximize the total area.....

Answer 2

Stuck on part B.

Answer 3

Total areas, r is radius of circle, s is side of square
A = π r² + s² ( 1)

From the perimeters:
P = 2π r + 4s = 8
-> s = ( 8 - 2π r ) / 4
= 2 - π r/2 (2)
Now plug (2) into (1), then take derivative to get min area: ...

Answer 4

@Phydeaux will you be fine here?

Answer 5

Yes, solved the problem using you solution. Thank you very much!

Answer 6

@Phydeaux Wow, thanks for being such a easy "customer" =)