Question

A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?

Answer 1

Let a piece of length l be cut from the given wire to make a square.
Then, the other piece of wire to be made into a circle is of length (28 − l) m.
Now, side of square = 1/4

Let r be the radius of the circle. Then 

The combined areas of the square and the circle (A) is given by,

By second derivative test, the area (A) is the minimum when 

Hence, the combined area is the minimum when the length of the wire in making the