#### Question In the given 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 = \\frac{22}{7}))

#### Video Explanation

#### Explanatory Answer

Radius of inner circle = 21cm

Radius of outer circle = 42cm

Area of the complete disc = area of outer circle – area of inner circle

= π(r_{outer})^{2} – π(r_{inner})^{2}

But an arc AB subtending 60° is not shaded.

So, area of shaded region = \\frac{300}{360}) × area of complete disc

= \\frac{5}{6}) (π(42)^{2} - π(21)^{2})

= \\frac{5}{6}) π(42^{2} – 21^{2})

= \\frac{5}{6}) π[(42 + 21)(42 – 21)]

= \\frac{5}{6}) π(63 × 21)

= \\frac{5}{6}) × \\frac{22}{7}) (63 × 21)

= 55 × 63

= 3465 cm^{2}