In figure 2, 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]

Given two concentric circles with centre O having radii 21 cm and 42 cm.

We know that area between the circles = π (R² – r²)

⇒ Area = (22/7) (42² – 21²)

= (22/7) (1323)

= 4158 cm²

Angle subtended by the arc in the inner circle = 60°

Area of the sector in the inner circle = 231 cm²

Angle subtended by the arc in the outer circle = 60°

Area of the sector in the outer circle = 924 cm²

Area of the portion of the sector in between the circles = 924 – 231 = 693 cm²

Area of the shaded portion = Area between the circles – area of the portion in between the circles

= 4158 – 693

= 3465

∴ The area of the shaded region is 3465 cm².