In the adjoining figure, radius of the circle is 7 cm and m (arc MBN)

1.	In the adjoining figure, radius of the circle is 7 cm and m (arc MBN) = 60° , find i. Area of the circle. ii. A(O-MBN). iii. A(O-MCN).
Answer» Given: radius (r) = 7 cm, m(arc MBN) = θ = 60° i. Area of circle = πr² = 22/7 × (7)² = 22 × 7 = 154 cm² ∴ The area of the circle is 154 cm² ii. Central angle (θ) = ∠MON = 60° Area of sector = θ/360 x πr² ∴ A(O – MBN) = 60/360 × 22/7 × (7)² = 1/6 × 22 × 7 = 25.67 cm² = 25.7 cm² ∴ A(O-MBN) = 25.7 cm² iii. Area of major sector = area of circle – area of minor sector ∴ A(O-MCN) = Area of circle – A(O-MBN) = 154 – 25.7 ∴ A(O-MCN) = 128.3 cm²

In the adjoining figure, radius of the circle is 7 cm and m (arc MBN) = 60° , find i. Area of the circle. ii. A(O-MBN). iii. A(O-MCN).

Answer»

Given: radius (r) = 7 cm,

m(arc MBN) = θ = 60°

i. Area of circle = πr²

= 22/7 × (7)²

= 22 × 7

= 154 cm²

∴ The area of the circle is 154 cm²

ii. Central angle (θ) = ∠MON = 60°

Area of sector = θ/360 x πr²

∴ A(O – MBN) = 60/360 × 22/7 × (7)²

= 1/6 × 22 × 7

= 25.67 cm²

= 25.7 cm²

∴ A(O-MBN) = 25.7 cm²

iii. Area of major sector = area of circle – area of minor sector

∴ A(O-MCN) = Area of circle – A(O-MBN)

= 154 – 25.7

∴ A(O-MCN)

= 128.3 cm²