A square of side x metres is bent in the form of a circle and later this circle is cut into two equal halves. One half is bent to form a square. Find the difference in the areas of circle and the square bent from the half cut circle if x=2. [4 MARKS]

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Solution

Process : 3 Marks
Result : 1 Mark

Given circle has perimeter of circle = 4x metres
Circle will be having a radius(r) = $\frac{4 x}{2 π}$
Area of the Circle so formed = $π \times (\frac{4 x}{2 π}) \frac{4 x}{2 π} m^{2} = \frac{4 x^{2}}{π}$
Circle which is half cut has a circumference of 2x.
Square bent from half circle has circumference of 2x metres.
Side of the square = $\frac{2 x}{4}$
Area of the square = $\frac{x}{2}$
Putting x = 2
Difference = $(\frac{16}{π}) - 1$

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