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10 Questions 10 Marks 6 Mins
Given:
Radius of circle = 14 cm
Central angle = 60°
Formula used:
Area of minor segment = \(πr^2 × \frac{θ}{360°} - \frac{1}{2}r^2sinθ\)
where r is the radius
and θ is the angle of the segment
Sin 60° = \(\frac{\sqrt3}{2}\)
Calculation:
According to the question,
Area of segment = \(\frac{22}{7} × 14^2 × \frac{60°}{360°} - \frac{1}{2} × 14^2sin60°\)
⇒ \(22× 28× \frac{1}{6} - 98× \frac{\sqrt3}{2}\)
⇒ 102.67 - 49 × 1.73
⇒ 102.67 - 84.87 = 17.79 ≈ 17.8 cm2
∴ The area of minor segment is 17.8 cm2
Alternate Method
Given:
Radius of circle = 14 cm
Central angle = 60°
Formula used:
Area of the circle = πr2
Area of sector = \(πr^2 × \frac{θ}{360°}\)
Calculation:
According to the diagram,
Area of the circle = πr2
⇒ 22/7 × (14)2 = 616 cm2
Area of the sector AOB = \(πr^2 × \frac{θ}{360°}\)
⇒ \(\frac{22}{7} × 14^2 × \frac{60°}{360°}\)
⇒ 616 × 1/6 = 102.67 cm2
Area of Δ AOB = \(\frac{\sqrt3}{4} \times (AO)^2\)
⇒ Area of the minor segment = Area of the sector AOB - Area of Δ AOB
⇒ 102.67 - 84.87 = 17.79 ≈ 17.8 cm2
∴ The area of minor segment is 17.8 cm2
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Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60∘. Also find the area of the corresponding major segment. [Use .π=22/7]
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