Question

In figure, OAPB is a sector of
Circle of radius 3.5cm with the
Centre at O and ✓AOB = 120
Find the length of OAPBO.
120​


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Answer 1

Given :----

• Angle AOB = 120°
• Radius AO = OB = 3.5cm .

To Find :----

• Length of OAPBO ..

Concept used :--------

• Length of OAPBO = Radius of Circle AO+OB + length of major arc of circle ...
• Length of major Arc = (Angle at centre/360°) × 2πr
• Angle of Major Arc = (360° - angle at minor Arc)
• π = 22/7 ..

__________________________

Calculation :-------

Putting all values we get,

→ length of both radius = 3.5 + 3.5 = 7cm

→ Length of major Arc = ((360°-120°)/360°) × 2 × 22/7 × 3.5

= (44/3) cm .

_____________________

Hence, Length of OAPBO = 7 + 44/3 = (65/3)cm or = 21(2/3)cm ..

_______________________________

Extra knowledge :-----

→ Area of Minor sector with angle @ is given by = (@/360°)×π×r² .. ( where r is radius of circle) .

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