What is a Circle and How to calculate the Area of a Circle?

In this article, we will check how to calculate the area of a circle. A circle is a round-shaped figure which has no corners and no edges. A circle is a plane figure with one center point. We can see a number of circles in our daily life in many different forms, like wheels, bangles, round rings, etc.

We can divide the circle majorly into 3 parts:
• Interior
• Exterior
• Boundary

Interior: Interior means any part and any point of the circle which is present inside the circle. In other words, all that portion and all that point are covered within the boundary of a circle.

Exterior: Exterior refers to that part and that point that is present outside the circle. In other words, all that point and all that parts are from outside the boundary point of a circle.

Boundary: The other part is the boundary. It includes all the points which lie on the boundary of a circle. Any point on the boundary of a circle has an equidistance from the center of a circle.

Area of Circle

The area of a circle means how much area is occupied by the circle at a given point or in a two-dimensional plane and in other words, we can also say that area is occupied within the boundary of a circle.

Area of a Circle
Area of a Circle

We can calculate the area of a circle by the given formula:

A= πr2

In which, ‘r’ is the radius of the circle and in other words, the radius of a circle is denoted by r.

The area of any region can be measured only in square units. For example, m2

The value of ‘π’ is 22/7 and 3.14.

We can also say that area of a circle is the measured area of a circle =

πD2/4

In this ‘D‘ is the diameter of a circle. The diameter of a circle is the longest chord of a circle. And it is denoted by D.

Diameter: Diameter is the straight line that passes through the center and touches both ending points of a circle.
It is calculated by the given formula:

D=2*R

And here, ‘R‘ is the radius of a circle. The diameter is always double the radius.


Radius: Radius is the half of the diameter of a circle and it is calculated by the given formula:

R=D/2

Area of Circle With Example,

  1. If the diameter of a circle is 10 cm and we want to calculate the radius of a circle. Then we can calculate radius by:
    Applying formula:
    R=D/2
    Diameter=10, then radius will be:
    R=10/2
    R=5cm

2. If the radius of a circle is 6cm and we want to calculate the diameter of a circle. Then we can calculate diameter by:
Applying formula:
D=R.2
Radius=6cm, then diameter will be
D=6.2
D=12cm.

Circumference of a circle:


The circumference of a circle is equal to the perimeter of a circle and in other words, the circumference of a circle is equal to the total length of the boundary of a circle or any object. We can calculate the circumference if a circle by applying the following formulas:

C=2πr

Where,
R is the radius of the circle
π is the constant mathematical value whose value is always 22/7 and 3.14.
The circumference of a circle is used to find the area of a circle.
We can find the area of a circle when the circumference of a circle is given by applying the following formula:

C2/4π

Here, C is the circumference of a circle. In other words, the area of a circle is=

(Circumference)2/4π

Arc of the Circle

The arc of the circle is any segment or any part of the circumference of a circle. In other words, any piece of the circle that lies between the two points is also known as the arc of the circle.

Major arc: Major arc means the longer side of the arc.

Minor arc: Minor arc means the shorter side of the arc.

Semicircular arc of the Circle: The semicircular arch of the circle means when the length of the arc is exactly equal to the half of a circle, then it is known as the semicircular arc of the circle.

Chord of a Circle

A chord is a straight line of the circle that is drawn by joining the two ends of the circle is known as the chord of a circle. In other words, a straight line segment whose end lies on any two points of the curve is known as a chord. A circle can have an infinite number of chords. The diameter is the longest chord of the circle. Any radius of the circle is also the chord of the circle.

Major segment: Major segment refers to that segment of the intercepted arc of the circle which is
greater than the semicircle.

Minor segment: Minor arc refers to that segment of the intercepted arc of the circle which is less
then the semicircle.

Area of a Circle With Examples

  1. Calculate the area of a circle whose radius is 7cm.
    Sol:
    We have given the radius of a circle=7cm.
    Then,
    By applying formula:
    Πr2
    =22/777
    =22*7
    =154cm

2. Calculate the area of a circle whose radius is 14cm
We have given the radius of a circle= 14cm.
Then,
By applying the formula:
Πr2
=22/71414
=22214
=616cm

3. Calculate the area of a circle whose diameter is 14cm
Sol:
Now, we have given the diameter of a circle. Then, firstly we calculate the
radius from the given diameter.
D= 14
R=D/2
R=14/2
R=7cm
Now, we calculate the area of a circle.
Area=πr2
=22/777
=22*7
=154cm

4. Find the circumference of a circle if the radius is 21.
Sol:
Now, we have to calculate the circumference of a circle.
The radius given is 21cm.
Then, by applying the formula of the circumference of a circle we get,
C=2πr
C= 222/721
C=2223
C= 132cm

5. If the longest chord of a circle is 28cm, then find the area and
circumference of the circle.
Sol:
The longest chord of a circle is also known as the diameter of the circle. It
means that diameter of a circle is 28cm.
Then the radius will be:
R=28/2
R= 14cm

Area of circle:
A=πr
2 A=22/71414
A= 22214
A=616cm

Circumference of the circle:
C=2πr
C=222/714
C=2222
C=88cm.

From the all above meanings and examples we come to know about circles, the diameter of a circle, the radius of a circle, arc, semicircle, chord, major segment, minor segments, etc. We also learn some of the examples to calculate the area and circumference of a circle.

The circumference and area of a circle?

The circumference of a circle is equal to the perimeter of a circle and in other words, the circumference of a circle is equal to the total length of the boundary of a circle or any object. The area of a circle means how much area is occupied by the circle at a given point or in a two-dimensional plane.

What is an area of a circle?

The area of a circle means how much area is occupied by the circle at a given point or in a two-dimensional plane. We can calculate the area of a circle by the given formula:
A= πr2

1 thought on “What is a Circle and How to calculate the Area of a Circle?”

Leave a Comment