# A wire of length 2 units is cut into two parts which are bent respectively to form a square of side=x units and a circle of radius=r units.  If the sum of the areas of the square and the circle so formed is minimum, then : Option 1) 2x = (π+4) r   Option 2)  (4−π) x = πr   Option 3)  x = 2r   Option 4)  2x = r

As we learnt in

Circle -

A circle is the locus of a moving point such that its distance from a fixed point is constant.

- wherein

Let the length of two parts be 'a' and '2-a'

and

where x is side of square

sum of Areas

of

Hence

Option 1)

2x = (π+4) r

Incorrect

Option 2)

(4−π) x = πr

Incorrect

Option 3)

x = 2r

Correct

Option 4)

2x = r

Incorrect

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