Topics
Similarity
- Properties of Ratios of Areas of Two Triangles
- Basic Proportionality Theorem
- Property of an Angle Bisector of a Triangle
- Property of Three Parallel Lines and Their Transversals
- Similarity of Triangles (Corresponding Sides & Angles)
- Relation Between the Areas of Two Triangles
- Criteria for Similarity of Triangles
- Overview of Similarity
Pythagoras Theorem
- Pythagoras Theorem
- Pythagorean Triplet
- Property of 30°- 60°- 90° Triangle Theorem
- Property of 45°- 45°- 90° Triangle Theorem
- Similarity in Right Angled Triangles
- Theorem of Geometric Mean
- Right-angled Triangles and Pythagoras Property
- Converse of Pythagoras Theorem
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Apollonius Theorem
- Overview of Pythagoras Theorem
Circle
- Circles Passing Through One, Two, Three Points
- Tangent and Secant Properties
- Secant and Tangent
- Inscribed Angle Theorem
- Intersecting Chords and Tangents
- Corollaries of Inscribed Angle Theorem
- Angle Subtended by the Arc to the Point on the Circle
- Angle Subtended by the Arc to the Centre
- Overview of Circle
Geometric Constructions
Co-ordinate Geometry
Trigonometry
- Trigonometric Ratios in Terms of Coordinates of Point
- Angles in Standard Position
- Trigonometric Ratios
- Trigonometry Ratio of Zero Degree and Negative Angles
- Trigonometric Table
- Trigonometric Identities (Square Relations)
- Angles of Elevation and Depression
- Relation Among Trigonometric Ratios
- Trigonometric Ratios of Specific Angles
Mensuration
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"/"diameter"` = π
circumference = π × diameter
= π × 2r (where r is the radius of the circle)
= 2πr
Circumference of a circle: 2πr
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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