A circle is a curve joining a set of points which are at same distance from a fixed point. Here, the fixed point is called the center of the circle and the fixed distance is called the radius of the circle.
If we divide the distance along the curve of the circle by its diameter then we always get a constant value which is very closed to 3.14159265358979323846….. Thus this value is rounded to 3.142. This value is represented by a Greek letter π.
i.e. π = 3.142.
The circumference of a circle is the distance around the circle. If C is the circumference of a circle and d is its diameter then by the above definition of π, we can write
π = C/d
Or C = πd
Or C = π (2r) = 2 πr. (because d=2r), where r is the radius of the circle.
Area of a circle:
The area of a circle is the number of square units inside the circle or it is the space occupied by the circle. In the following circle, we can count that the number of squares is 28.26. So, the area of the following circle is 28.26 square units.
But it is not always possible to count the number of squares inside the circle, especially in case of larger circles. In that case, we have a formula which can be used to find the area of circles.
If r is the radius of the circle then the area of the circle A = πr2.
Since r = d/2, where d is the diameter of the circle, the above formula can be re-written as
A = π (d/2)2.
Or A = πd2/4
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