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 lengths of the two pieces so that the combined area of the circle and the square is minimum?
Let the length of side of square be a and radius of circle be r.
It is given that wire is cut into two parts to form a square and a circle
Therefore, perimeter of square + circumference of circle = length of wire
4a + 2πr = 28
a = 
…1
Let us assume area of square + area of circle = S
S = a2 + πr2
S = 
+ πr2 (from equation 1)
Condition for maxima and minima
…2
So, for 
>0
This is the condition for minima
From equation 1
a = 
Substituting from equation 2
a = 
a = 
a = 
Hence, radius of circle and length of square be 
and
respectively.