Question

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

(a) 2x = (pi + 4)r

(b) (4 - pi)x = pi r

(c) x = 2r

(d) 2x = r

Answer 1

Correct option (c) x = 2r

Explanation:

According to given information, we have Perimeter of square + Perimeter of circle = 2 units

Now, let A be the sum of the areas of the square and the circle. Then,