An arc of a circle whose radius is 21 cm subtends an angle of measure 120 at the centre. Find the length of the arc and area of the sector.
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Sector angle ( x° ) = 120°
radius ( r ) = 21 cm
length of the arc = l
i ) l = ( x/360 ) × 2πr
= ( 120/360 ) × 2 × ( 22/7 ) × 21
After cancellation , we get
l = 44 cm
ii ) Area of the sector ( A ) = (x/360)πr²
=> A = ( 120/360 ) × ( 22/7 ) × ( 21 )²
= ( 1/3 ) × ( 22/7 ) × ( 21 × 21 )
= 462 square cm
••••
radius ( r ) = 21 cm
length of the arc = l
i ) l = ( x/360 ) × 2πr
= ( 120/360 ) × 2 × ( 22/7 ) × 21
After cancellation , we get
l = 44 cm
ii ) Area of the sector ( A ) = (x/360)πr²
=> A = ( 120/360 ) × ( 22/7 ) × ( 21 )²
= ( 1/3 ) × ( 22/7 ) × ( 21 × 21 )
= 462 square cm
••••
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