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subject: Introduction To Area Of A Sector Of A Circle [print this page]

Sector of a circle is a region of the circle enclosed between two radii and the circumference. For smaller area, sector is known as minor sector of the circle and the larger area is known as the major sector.

In figure below we have,

Angle formed by the arc with the centre of the circle =

radius = r

Angled formed by the arc

Formula for Area of a Sector of a Circle

Let,

radius = r

angle formed by the arc at the centre =

angle of the circle = 2

area of the circle = r 2

Area of sector of a circle = r 2 * ( / 2 )

= ( r 2 * ) / 2

= ( r 2 * ) / 2

Area of a sector of a circle= ( r 2 * ) / 2 = 1 / 2 *( r 2 * ) ( in radian)

If angle is in degrees then,

= 360 o

Area of sector of a circle = r 2 * ( / 360)

Examples on Area of a Sector of a Circle

Ex:1 The angle made by an arc at the centre of the circle with radius 14 cm is 60 0. Find the area of the sector .

Sol: Given radius = r = 14, angle = = 60 0

area of sector

We know, area of sector = r 2 * ( / 360)

plug in the values of r and ,

Area of sector = (14) 2 * ( 60 / 360) ( take = 22 / 7 )

= 22/ 7 * (14) 2 * ( 60 / 360)

= (22 * 14 * 14 ) / 7 * ( 1 / 6) ( because 360 = 60 x 6)

= ( 22 * 14 * 2) * ( 1 / 6) ( because 14 = 7 x 2 )

= ( 22 * 14 ) * ( 1 / 3) ( because 6 = 3 x 2)

= ( 308 ) / 3

= 102. 67 cm 2

Area of sector = 102.67 cm 2

Ex:2 The angle made by an arc at the centre of the circle be 45 0 and area of the sector be 98 cm 2, then find the radius of the circle. ( 249.681)

Sol: Given, angle = = 45 0

area of sector = 98 cm 2

= 3.14

radius = r = ?

Area of a sector = r 2 * ( / 360)

Plug in the values,

98 = 3.14 * r 2 * ( 45 / 360)

98 = 3.14 * r 2 * ( 5/ 40)

98 = 3. 14 * r 2 * ( 1 / 8 )

multiply throughout by ( 8 / 3.14 ) ,

98 * 8 / 3.14 = ( 3.1 4 * r 2 ) / 8 * ( 8 / 3.14)

784 / 3.14 = r 2

249.681 = r 2

taking square roots on both sides, we get,

15.80 = r

Ex:3 Let area of sector be 100 cm 2 and radius of the circle be 15, then find angle formed by the arc at the centre of the circle? ( take = 3.14).

Sol: Given, area of sector of a circle = 100 cm 2

radius = 15

= ?

Area of sector = r 2 * ( / 360)

100 = 3.14 * 15 2 * ( / 360)

100 = 3.14 * 225 * ( / 360)

100 = 706.5 * ( / 360)

100 = (706.5 * ) / 360

100 = ( 706.5 / 360 ) *

multiply throughout by 360 / 706.5 ,

100 * (360 / 706.5) = ( 760.5 / 360 ) * (360 / 706.5) *

100 * 0.50955 =

50.96 =

by: johnharmer

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