Question

find the area of the sector of a circle whose radius is R and length of the arc is l

Answer 1

Solution :


Given :

✏ Radius of Circle( Sector) = R

✏ Length of arc of Circle = l

To Find : Find the area of Sector ?

Solution :

Area of Sector = (Radius) × (Length of arc ) / 2


Area of Sector = R × l /2


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Let the Length of arc is l and it's Radius is r

Area of Sector = πr²∅/360°


Hence, Required Formula of Area of Sector = 1/2 × (R) × (l) .

Answer 2

SECTOR OF A CIRCLE:

The region enclosed by two radii and the corresponding arc of a circle is called the sector of a circle. The sector containing minor Arc is called minor sector and the sector containing major arc is called major sector. Angle of minor sector is less than 180° and Angle of major sector is more than 180°.The sum of angles of major and minor sector is 360°.


SOLUTION:
If the radius of a circle is r and length of the arc is l, then

Length of the arc (l) = (θ /360) ×2 πr……(1)
Length of the arc (l) = (θ /180) × πr

Area of sector = (θ /360) ×πr²
Area of sector = ½ ×r (θ / 180) ×πr
Area of sector =( ½) lr [ from eq 1]

Hence , the Area of sector = ( ½) lr sq units.

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