Q. 73.7( 3 Votes )

# 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?

Answer :

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 = a^{2} + πr^{2}

S = + πr^{2} (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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