Suppose you decide to cut the wire into two pieces (not necessarily the same length) to shape into two circles. Write a function A ( x ) which models the total area of the two circles in terms of x , the length of one of the pieces of wire. (It may be helpful to use for a circle A = πr 2 and C = 2 πr ). Then find the length x that will minimize the total area.

Explanation:

Let the area of one circular side be given by the formula :

However, the wire is a solid cylinder, then it means that the total area is 2 × =

However, there is the surface area to consider. This is the curved area of the wire. This is given as:

The length is x.

The breadth is calculated as follows  - the length of the circle =

Then the area = lb

                        =

Therefore, the total area is given as

                       =

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