A piece of wire 6 m long is cut into two pieces. One piece is bent into the shape of a circle of radius r and the other is bent into a square of side s.

Question

A piece of wire 6 m long is cut into two pieces. One piece is bent into the shape of a circle of radius r and the other is bent into a square of side s. How should the wire be cut so that the total area enclosed is:

a) a maximum? r = __ and s =__

b) a minimum? r = __ and s =__

Answer 1

s represents the side of the square

s² represents the area of the square

6 - 4s rerpresesnts the circumference of the circle

2πr represents the circumference of the circle

2πr = 6 - 4s

r = (3 - 2s) / π

πr² represents the area of the circle

π[(3 - 2s) / π]² represents the area of the circle

TA = s² + π[(3 - 2s) / π]²

Can you simplify (Algebra 1) and set first derivative to zero?