Circle Formulas

Circle:

At this stage, we study plane figures which are in 2 dimensions. Circle is one of them. Circle is said to be an important part of geometry because it has a wide range of applications. When we see around many objects have circular portion. Take an example of a water bottle, from its cover to bottom it is circular. To make it, there must be requirement of knowledge of circle and circle formulas.

Definition of circle:

We can define circle as closed figure round in shape. Or,

Circle is a collection of points which is equidistant from a given fixed point. Or,

Circle is a curve which follows a path which is all round equidistant from a fixed point.

Terms used in circle:

Radius: The line segment joining the centre to any point on the circle.

Diameter: The line segment joining two points on the circle and passes through centre is called diameter. Or, say the longest chord of circle.

Chord: The line segment joining any two point on the circle is called chord.

Arc: A part of circumference of circle whose end points joined by chord. Smaller part is minor arc and larger part is major arc.

Sector: The space covered by arc and two radius in a circle is Sector.

Tangent: A straight line which only touches the circle and is in the plane of circle.

 Circumference: The length of curved path of circle is called circumference.

Circle Formulas:

r is symbol for radius of circle.

d is symbol for diameter of circle.

c is symbol for circumference of circle.

Circle formulas are:

1. Diameter of circle = 2r
2. Circumference of circle = 2πr (where π = \(\frac{22}{7}\))
3. Area of circle = πr²

Extended circle formulas:

1. Length of arc = \(\frac{ϴ}{360⁰}\) x 2πr (where ϴ = angle subtended by arc at centre)
2. Area of sector = \(\frac{ϴ}{360⁰}\) x πr² (where ϴ = angle subtended by sector at centre)

Examples of circles:

1. If the diameter of a circle is 14 cm, Find the area of circle.

Solution:

D = 2r
r = D/2
r = 7 cm
Area = πr²
Area= \(\frac{22}{7}\)x 7^2
=154 cm²

2. If circumference of circle is 308cm. Find the area of circle.

Solution:

Circumference = 2πr = 308 cm
r = \(\frac{308}{2π}\) = 49
Area = πr^2
=\(\frac{22}{7}\) x (49)² = 7546 cm²