Q7 of 137 Page 19

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.


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