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Question

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]


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×x


The circle will have the same perimeter as that of the square = 4×x metres
Circle will be having a radius(r) = 4x2π
Area of the Circle so formed 
= π×(4x2π)4x2πm2=4x2π

The circle which is half cut has a circumference of 2x.
Square bent from half circle has the circumference of 2x meters.
Side of the square = 2x4
 Area of the square = x24
Putting x = 2
We get the area of the circle
= 4π×22  = 5.09 m2

The area of the square = 44 = 1m2

The difference between the area of the circle and the area of the square
= 5.09 - 1 = 4.09 m2

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