# 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 a circle with angle θ = θ/360° × πr^{2}

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

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

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

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

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}

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 12

**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

**Summary:**

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 ∠AOB = 30° is 308/3 cm^{2}.

**☛ Related Questions:**

- In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in Fig. 12.24. Find the area of the design.
- In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.
- Fig. 12.26 depicts a racing track whose left and right ends are semicircular. Fig. 12.26 The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find :(i) the distance around the track along its inner edge(ii) the area of the track.
- In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

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