Circle Formula

We may have come across many objects in our daily life which is round in shape. Some objects of this shape are wheels of a vehicle, bangles, dials of clocks, coins, etc. In a clock, we have observed that the second’s hand goes around the dial of the clock. It is making a round path around the fixed pivot. This pivot is known as a circle. This path traversed by the tip of the second’s hand is called a circle. In this article, we will discuss circles, some other related terms and circle formula with examples. Let’s start learning!

Circle Formula

What is a circle?

A circle is a particular shape of the objects. A circle is a type of closed shape. It is the set of all points in a plane that are at a given distance from a given point. So, it is the curve traced out by a point that moves in a plane in such a way so that its distance from the given point is constant.

It is defined as the set of points in a plane placed at the equal distance from a single pivot point, called the center of the circle. It is a fact that the circle represents a two-dimensional plane. Its three-dimensional figure is known as a sphere. In this shape, no vertex or edge exists.

Some terms related to this shape are as follows:

1. Center: It is a point as a pivot in the circle. It is used to draw the circle.
2. Circumference: It is the set of points that are at equal distance around the center of the circle.
3. Radius: It is the distance from the center to any point on the circumference.
4. Diameter: It is the distance between any two points on the circumference measured through the center. It is double in the length that the length of the radius.
5. Area: Area of the circle describes the amount of space covered by the circle. So, it will give the coverage of circle as a two-dimensional plane.

Diagram:

Source: en.wikipedia.org

 Where,

r	the radius of the circle.
d	the diameter of the circle.
C	circumference of the circle.

Circle Formula:

1. The diameter of the Circle is computed as,

D = 2 × R

Where,

D	The diameter of a Circle
R	Radius of circle

 

2. Circumference of the circle is computed as,

C = 2 × \(\pi\) × R

Where,

C	Circumference of circle
R	Radius of circle

 

3. Area of the circle is computed as,

A = \(\pi\) × R²

Where,

A	Area of circle
R	Radius of circle

Solved Examples on Circle Formula 

Q. A circular ground has a diameter of 800 m. Calculate the area of the circle.

Solution:

First we have to find radius of the circle as,

R = \(\frac{D}{2}\)

i.e R = \(\frac{800}{2}\)

R = 400 m

Now,

Area of circular ground,

A = \(\pi\) × R²

= \(\pi\) × (400)²

=  \(\frac{22}{7}\) × 400 × 400

= 502857.14 sq m

1. Find the area of the circle with length of circumference as 440 cm.

Solution:

First find the radius of the circle as,

C= 2 × \(\pi\) × R

i.e. R = \(\frac{C}{2 × \(\pi\)}\)

= \(\frac{440}{2 × 7}{22}\)

= 70 cm

Now, find the area of the circle as,

A = \(\pi\) × R × R

= \frac{22}{7} × 70 × 70

=15400 sq cm.