SSC (English Medium) Class 10th Board ExamMaharashtra State Board
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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. - SSC (English Medium) Class 10th Board Exam - Geometry

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ConceptTangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers

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.
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