Area of Sector


 
 
Concept Explanation
 

Area of Sector

Area of sector

The circular region enclosed by two radii and the corresponding arc is called a sector of the circle.

Applying the unitary method and taking the whole area of the circle (of angle 360^{circ}) as pi r^2, we can obtain the required area as

Area ;of ;the; sector; of; angle ;theta =frac{theta }{360}times pi r^{2}

Example    The perimeter of a certain sector of a circle of radius 5.6 m is 27.2 m. Find the area of the sector.

Solution   Let  theta ^{circ} be the angle subtended by the arc AB at the centre. We have

                                  l=(frac{pi }{180}theta )r

we are given

                                 r+r+l=27.2  

                               5.6 + 5.6 + l = 27.2

                                        11.2 + l = 27.2

                                                   l = 27.2-11.2= 16         

Rightarrow                          frac{pi r theta }{180} =16

theta =16 X frac{180}{pi r}= 16 X frac{180}{pi; X ;5.6}

Area ;of ;the; sector; of; angle ;theta =frac{theta }{360}times pi r^{2}

=frac{16 X 180} {pi X 5.6} ; X frac{1}{360} times pi ;X; 5.6; X; 5.6=frac{16}{2};X ;5.6= 8;X; 5.6 = 44.8m^2

 

Sample Questions
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Question : 1

The area of a sector of a circle of radius 16 cm cut off by an arc which is 18.5 cm long is:

Right Option : B
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Explanation
Question : 2

If the area of a minor sector of a circle of radius 5 m is 22 m^2, the area of the corresponding major sector so formed is

Right Option : B
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Explanation
Question : 3

The area of a sector of perimeter 45 cm and radius 6 cm is ________________________

Right Option : D
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Explanation
 
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