# AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region

**Solution:**

We use the formula for the area of the sector of a circle to solve the problem.

Area of the shaded region = Area of sector ABO - Area of sector CDO

Areas of sectors ABO and CDO can be found by using the formula of Area of a sector of angle θ = θ/360° × πr^{2}

Here, r is the radius of the circle and angle with degree measure θ

For both the sectors ABO and CDO angle, θ = 30° and radii 21 cm and 7 cm respectively.

Radius of the sector ABO, R = OB = 21 cm

Radius of the sector CDO, r = OD = 7 cm

For both the sectors ABO and CDO angle, θ = 90°

Area of shaded region = Area of sector ABO - Area of sector CDO

= θ/360° × πR^{2} - θ/360° × πr^{2}

= θ/360° × π (R^{2} - r^{2})

= 30°/360° × 22/7 ((21 cm)^{2} - (7 cm)^{2})

= 1/12 × 22/7 × (441 cm^{2} - 49 cm^{2})

= 11/42 × 392 cm^{2}

= 308/3 cm^{2}

**Video Solution:**

## AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region

### NCERT Solutions Class 10 Maths - Chapter 12 Exercise 12.3 Question 14:

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region

The area of the shaded region if AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and center O is 308/3 cm^{2}