Parts of Circle

The parts of Circle are Diameter,Radius,Arc and Sector.

Relation between diameter and radius

Diameter = 2 x radius

Or radius = r = d / 2.

Circumference ( C ) : The length of a boundary of a circle.

C = 2 Πr

Or C = Π D

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Examples

1) Radius = 4 cm, find the diameter.

Solution :
Diameter = 2 x radius

⇒ Diameter = 2 x 4

⇒ Diameter = 8 cm.

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2) Diameter = 6.4 cm, find the radius.

Solution :
radius = r = d / 2.

⇒ radius = 6.4/2

⇒ radius = 3.2 cm

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2)If the radius of circle is 1.5 cm then find the diameter and the circumference.

Solution :
Diameter = D = 2 r

D = 2 x 1.5

D = 3 cm.

Circumference = C = &pie;D

C = 3.14 x 3

C = 9.42 cm

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Some more parts of circle are as follows:

Arc : A part of a circle between any two points on the circle.

There are two types of arcs 1) Minor arc 2) Major arc.


Here PQR is the minor arc and PR is a major arc.

As arc is a part of a circle so,

Length of a minor arc = Π rθ / 180

Length of major arc = 2Πr - Π rθ / 180

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Examples

1) Find the length of arc of radius 6 cm and angle formed by the two radii is 60⁰.

Solution :
r = 6 cm , θ = 60⁰ and Π = 3.14

Length of a minor arc = Π rθ / 180

Length of a minor arc = ( 3.14 x 6 x 60 ) / 180

Length of arc = 6.28 cm

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2) Sector : The region enclosed by two radii and an arc.

Area ( minor sector ) = Πr²θ / 360

Area ( major sector) = Πr² - Πr²θ / 360

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Example : Find the area of sector whose radius is 8 cm , angle θ 30⁰ and Π = 3.14.

Solution :
r = 8 cm , θ = 30⁰ and Π = 3.14

Area of sector = Πr²θ / 360

Area = (3.14 x 8² x 30 ) / 360

Area of sector = 16.75 cm²

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Circles

• Circles
• Parts of Circle
• Arc and Chords
• Equal Chords of a Circle
• Arc and Angles
• Cyclic Quadrilaterals
• Tangent to Circle
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