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Course / Category - 10th NTSE

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NTSE

10th NTSE

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Concept Detail

Maths / Mensuration / Area of Sector

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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

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

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

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

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

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Available Online Courses for selected Class / Category

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₹17200 ₹12000 + Taxes

Area of Sector

₹17200 ₹12000 +
Taxes