Question

In Fig. 7, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and

3.5 cm and centre O. If ∠POQ = 30°, then find the area of the shaded region. [User`22/7`]

Answer 1

PQ and AB are the arcs of two concentric circles of radii 7 cm and 3.5 cm respectively.

Let r₁and r₂ be the radii of the outer and the inner circle respectively.

Suppose θ be the angle subtended by the arcs at the centre O.

Then r₁ = 7 cm, r₂ = 3.5 cm and θ = 30°

Area of the shaded region

= Area of sector OPQ − Area of sector OAB

`=O//360^@pir_1^2-O//360^@pir_2^2`

`=O//360^@pi(r_1^2-r_2^2)`

`=30^@/360^@xx22/7p[(7cm)^2-(3.5)^2]`

`=1/12xx22/7xx(49-12.25)cm^2`

`=9.625 cm^2`

Thus, the area of the shaded region is 9.625 cm².