A square of side ' $x$ ' meters 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 the circle and the square bent from the half cut circle if $x$ = 2. [4 MARKS]

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Solution

Formula: 1 Mark
Application: 2 Marks
Answer: 1 Mark

Given that
A square of side ' $x$ ' meters is bent into a circle.
The perimeter of the square = $4 \times x$

The circle will have the same perimeter as that of the square = $4 \times x$ metres
Circle will be having a radius(r) = $\frac{4 x}{2 π}$
Area of the Circle so formed
= $π \times (\frac{4 x}{2 π}) \frac{4 x}{2 π} m^{2} = \frac{4 x^{2}}{π}$

The circle which is half cut has a circumference of 2 $x$ .
Square bent from half circle has the circumference of 2 $x$ meters.
Side of the square = $\frac{2 x}{4}$
Area of the square = $\frac{x^{2}}{4}$
Putting x = 2
We get the area of the circle
= $\frac{4}{π} \times 2^{2}$ = 5.09 $m^{2}$

The area of the square = $\frac{4}{4}$ = 1 $m^{2}$

The difference between the area of the circle and the area of the square
= 5.09 - 1 = 4.09 $m^{2}$

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A square of side 'x' meters 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 the circle and the square bent from the half cut circle if x = 2. [4 MARKS]

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