Question 107

A wire of length 44 cm is first bent to form a circle and then rebent to form a square. The difference of the two enclosed areas is

Solution

Let radius of circle be $$r$$ and side of square be $$a$$

=> Circumference of circle = $$2 \pi r = 44$$

=> $$r = 7 cm$$

Since, the circular wire is bent to form square, => both of their perimeters are equal

=> Perimeter of square = $$4a = 44$$

=>$$a = 11 cm$$

Now, area of circular wire = $$\pi r^2$$

= $$\frac{22}{7} * 7^2 = 154 cm^2$$

Area of square = $$a^2$$

= $$11^2 = 121 cm^2$$

=> Required difference = 154-121 = $$33 cm^2$$


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