Topics
Number Systems
Algebra
Geometry
Trigonometry
Statistics and Probability
Coordinate Geometry
Mensuration
Internal Assessment
Real Numbers
Pair of Linear Equations in Two Variables
 Linear Equation in Two Variables
 Graphical Method of Solution of a Pair of Linear Equations
 Substitution Method
 Elimination Method
 Cross  Multiplication Method
 Equations Reducible to a Pair of Linear Equations in Two Variables
 Consistency of Pair of Linear Equations
 Inconsistency of Pair of Linear Equations
 Algebraic Conditions for Number of Solutions
 Simple Situational Problems
 Pair of Linear Equations in Two Variables
 Relation Between Coefficient
Arithmetic Progressions
Quadratic Equations
 Quadratic Equations
 Solutions of Quadratic Equations by Factorization
 Solutions of Quadratic Equations by Completing the Square
 Nature of Roots of a Quadratic Equation
 Relationship Between Discriminant and Nature of Roots
 Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
 Application of Quadratic Equation
Polynomials
Circles
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
 Tangent to a Circle
 Number of Tangents from a Point on a Circle
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Triangles
 Similar Figures
 Similarity of Triangles
 Basic Proportionality Theorem (Thales Theorem)
 Criteria for Similarity of Triangles
 Areas of Similar Triangles
 Rightangled Triangles and Pythagoras Property
 Similarity of Triangles
 Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
 Triangles Examples and Solutions
 Angle Bisector
 Similarity of Triangles
 Ratio of Sides of Triangle
Constructions
Heights and Distances
Trigonometric Identities
Introduction to Trigonometry
Probability
Statistics
Lines (In Twodimensions)
Areas Related to Circles
Surface Areas and Volumes
 Concept of Surface Area, Volume, and Capacity
 Surface Area of a Combination of Solids
 Volume of a Combination of Solids
 Conversion of Solid from One Shape to Another
 Frustum of a Cone
 Concept of Surface Area, Volume, and Capacity
 Surface Area and Volume of Different Combination of Solid Figures
 Surface Area and Volume of Three Dimensional Figures
definition
Circumference of a circle: The circumference or the perimeter of a circle refers to the measurement of the border across any 2D circular shape including the circle.
formula
Circumference of a circle = 2πr
notes
Circumcircle or Perimeter of a circle:

The word perimeter means a path that surrounds an area.

It comes from the Greek word 'peri,' meaning around, and 'metron,' which means measure.

Perimeter can be defined as the path or the boundary that surrounds a shape. It can also be defined as the length of the outline of a shape.

The circumference or the perimeter of a circle refers to the measurement of the border across any 2D circular shape including the circle.

Circumference of a circle bears a constant ratio with its diameter. This constant ratio is denoted by the Greek letter π (read as ‘pi’).
In other words,`"circumference"/"diameter" = π`
or, circumference = π × diameter
= π × 2r....................(where r is the radius of the circle)
= 2πr.
π is an irrational number and its decimal expansion is nonterminating and nonrecurring (nonrepeating).
However, for practical purposes, we generally take the value of π as `22/7` or 3.14, approximately.
Example
What is the circumference of a circle of diameter 10 cm (Take π = 3.14)?
Diameter of the circle (d) = 10 cm
Circumference of circle = πd
= 3.14 × 10 cm
= 31.4 cm
So, the circumference of the circle of diameter 10 cm is 31.4 cm.
Example
Find the perimeter of the given shape (Take π = `22/7`).
The outer boundary, of this figure, is made up of semicircles.
Diameter of each semicircle is 14 cm.
We know that:
Circumference of the circle = πd
Circumference of the semicircle = `1/2`πd
= `1/2 xx 22/7` × 14 cm
= 22 cm
Circumference of each of the semicircles is 22 cm
Therefore, perimeter of the given figure = 4 × 22 cm = 88 cm.
Example
Sudhanshu divides a circular disc of radius 7 cm in two equal parts. What is the perimeter of each semicircular shape disc? (Use π = `22/7`)
Given that radius (r) = 7 cm.
We know that the circumference of circle = 2πr
So, the circumference of the semicircle = `1/2` × 2πr = πr
= `22/7` × 7 cm
= 22 cm
So, the diameter of the circle =2r = 2 × 7 cm = 14 cm
Thus, perimeter of each semicircular disc = 22 cm + 14 cm = 36 cm.
Example
The radius of a circular plot is 7.7 metres. How much will it cost to fence the plot with 3 rounds of wire at the rate of 50 rupees per metre?
Circumference of circular plot = 2πr = `2 xx 22/7 xx 7.7` = 48.4
Length of wire required for one round of fencing = 48.4 m.
Cost of one round of fence = length of wire × cost per metre.
= 48.4 × 50
= 2420 rupees.
Cost of 3 rounds of fencing = 3 × 2420 = 7260 rupees
Example
The radius of the wheel of a bus is 0.7 m. How many rotations will a wheel complete while traveling a distance of 22 km?
Circumference of circle = πd = `22/7` × 1.4 = 4.4 m
When the wheel completes one rotation it crosses a distance of 4.4 m., (1 rotation = 1 circumference)
Total number of rotations = `"distance"/"circumference"`
= `(22000)/(4.4)`
= `(220000)/(44)`
= 5000
A wheel completes 10,000 rotations to cover a distance of 22 km.
Video Tutorials
Shaalaa.com  Area Related to Circles part 6 (Example)
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