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Question:

In Figure, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. [Use π=22/7]

Solution:

Given: Radii of inner circle = 21 cm = r
Radii of outer circle = 42 cm = R
∠AOB = θ = 60°
Area of ring = π(R² - r²)
Area of sector = θ/360 πr²
The area of shaded region = Area of ring – Area of ABDC
= Area of ring – [Area of sector of outer circle – Area of sector of inner circle]
= π(R² - r²) – π(R² - r²) * (θ/360)
= π[R² - r²](1 - θ/360)
= 22/7[42² - 21²](1 - 60/360)
= 3465 cm²