# Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠ AOC = 40°

**Solution:**

We use the concepts related to areas of sectors of circles and also we use concepts of concentric circles.

In a circle with radius r and the angle at the centre with degree measure θ, area of the sector = θ/360° × πr^{2}

The area of the shaded region can be calculated by subtracting the area of the sector of the smaller circle from the area of the sector of the larger circle.

Area of shaded region ABDC = Area of sector ACO - Area of sector BDO

Radius of the larger circle, R = OA = 14cm

Radius of the smaller circle, r = OB = 7cm

The angle at the centre, θ = 40°

Area of shaded region ABDC = Area of sector ACO - Area of sector BDO

= θ/360° x πR^{2} - θ/360° x πr^{2}

= θ/360° π (R^{2} - r^{2})

= θ/360° π (R + r )(R - r)

= 40°/360° × 22/7 × (14 + 7) (14 - 7)

= 1/9 × 22/7 × 21 × 7

= (22 × 21 × 7)/(9 × 7) cm^{2}

= (22 × 7)/3

= 154/3 cm^{2}

**Video Solution:**

## Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠ AOC = 40°

### NCERT Solutions Class 10 Maths - Chapter 12 Exercise 12.3 Question 2

Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠ AOC = 40°

The area of the shaded region if the radii of the two concentric circles with center O are 7 cm and 14 cm respectively and ∠AOC = 40° is 154/3 cm^{2}