Arc Length of Sector


 
 
Concept Explanation
 

Arc Length of Sector

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

length ;of ;an ;arc ;of; a; sector; of; angle;theta =frac{theta }{360}times 2pi r.

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

Solution:   r + r + l = 27.2

             5.6+ 5.6 + l = 27.2

                    11.2+ l = 27.2

                               l = 27.2 - 11.2= 16 m

Example: Find the length of the arc of a sector subtending an angle of 60 degree at the centre. The Radius being 12 m.

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

                                             l=frac{theta }{360}X 2pi r=frac{pi ;r;theta} {180}

                                            l=frac{60 }{360}X 12=2m

Sample Questions
(More Questions for each concept available in Login)
Question : 1

The area of a sector of a circle of radius10 cm cut off by an arc which is 22 cm long is ______________

Right Option : B
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Explanation
Question : 2

the length of an arc, which subtends an angle of 120^o at the centre of a circle, with radius 63cm is  ________________

Right Option : B
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Explanation
Question : 3

The area of a sector of circle of radius 9 cm is 9 pi ; cm^2. What will be the length of the arc of this sector ?

Right Option : A
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Explanation
 
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