Area of a Circle Formula

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The Formula of a Circle

The area of a circle refers to the region which is occupied by a circle in the 2D plane. We can determine it using the area of sector formula, which is A = πr2. Here, r refers to the radius of the circle and the unit of the area is in the square unit like cm2, m2, etc. We use this formula to measure the space which is occupied by either a circular plot or a field. In this article today, we will discuss the area of circle definition, the area of a circle equation, its circumference and surface area in detail.


What is a Circle

A circle is known as a closed plane geometrical shape. Technically, it is the locus of a point that moves around a fixed point at a fixed distance that is away from that point. A circle is basically a closed curve that has its outer line at an equal distance from the centre. This fixed distance from the central point is known as the radius of the circle. In our day to day life, we often see many examples like a pizza, wheel, etc. Let us learn about these terms in regards to a circle.


Radius

The radius of the circle is known as the line that tends to join the centre of the circle to its outer boundary. It is generally represented either by the symbol ‘r’ or ‘R’. In the formula of the area and the circumference of a circle, radius has an important role.


Diameter

The diameter of the circle is referred to as the line that tends to divide the circle into two equal portions. In a simpler way, we can say that it is twice the radius of the circle and is represented by either the symbol ‘d’ or ‘D’. Hence, we can say that

d = 2r or 

D = 2R

If we know the diameter of the circle, we can easily calculate the radius of the circle.

r = d/2or

R = D/2


Area of a Circle Definition

Any given geometrical shape possesses its own area. This area is referred to as the region which is occupied by the shape in a 2D plane. If we talk about the area of a circle, it is the area covered by a complete cycle by the radius of the circle on a 2D plane. We can calculate the area of the circle using a formula, so let us see what it is.


Area of a Circle Formula

Consider a circle with radius r.

(Image to be added soon)

In the figure above, we can see the circle having a radius ‘r’ from the centre ‘o’ to the boundary of that circle. Hence, the area of this circle A equals the product of pi and the square of the radius. It is given by the formula: 

Area of a Circle, A = πr2square units

Here, 

The value of pi, π = 22/7 or 3.14 and 

r is the radius of the circle


Circumference of A Circle

The perimeter of a closed figure is known to be the length of its total boundary. When it comes to the circles, the perimeter is called by a different name. It is referred to as the ‘circumference’ of the given circle. This circumference is known as the total length of the boundary of the given circle. If we open the circle and form a straight line, the length of the straight line that we get is the circumference. For defining the circumference of a circle, we need to know a term called ‘pi’. Consider the circle shown below having its centre at O and radius r.

(Image to be added soon)

The perimeter of the circle equals the length of its total boundary. The length of the rope that wraps around its boundary is equal to its circumference. We can measure this by using the formula given below.

Circumference / Perimeter of a circle = 2πr units

Here, r is known as the radius of the given circle.

The symbol π, read as ‘pi’, is referred to as the ratio of the circumference of the given circle to its diameter. This ratio would be the same for all circles. Consider, for example, a circle having radius ‘r’ and circumference ‘C’. in this circle,

π = Circumference/Diameter

π = C/2r

Hence, C = 2πr

The same concept is shown in the figure below.

(Image to be added soon)

FAQ (Frequently Asked Questions)

1. How to find the area of a circle?

Determining the area of the circle includes using different formulas. We can find the area of the circle with the formulas shown as follows.


  1. In terms of the radius ‘r’, 

             Area A = π x r2


  1. In terms of the diameter ‘d’,

            Area A = (π/4) x (d/2)


  1. In terms of the circumference ‘C’,

           Area A = C2/


2. What is the formula to find the surface area of a given circle?

A circle is referred to as the 2D representation of the sphere. The total amount of area which is taken inside the boundary of a given circle is referred to as the surface area of that circle. When we need to determine the area of the circle, it means that we need to find the surface area of that circle. Often, the volume of the circle would define the area of the circle as well.


When we have the length of the diameter or the radius or the circumference of the circle, we can find the surface area of the circle by using the surface area formula. This surface area of the circle is represented in terms of square units.


The surface area of the circle is given by, 


A = πr2