#### Question

Radius of a sector of a circle is 21 cm. If length of arc of that sector is 55 cm, find the area of the sector.

#### Solution

It is given that radius of circle = 21cm

length of arc of that sector is 55 cm

The ratio arc length of sector to circumference of circle is same as ratio of area of sector to area of circle

`"arc length"/ "circumference" = 55/(2πr)`

The area of sector is `55/(2πr)`of total area of circle with radius 21cm

To find area of circle with radius 21cm

Area = `πr^2`

__To find the area of sector__

Area of sector =`(55/(2pr)) xx πr^2 = (55r)/2 = (55 xx 21)/2 = 577.5 "cm"^2`

Therefore sector area = `577.5 "cm"^2`

Is there an error in this question or solution?

Solution Radius of a Sector of a Circle is 21 Cm. If Length of Arc of that Sector is 55 Cm, Find the Area of the Sector. Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers.