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° × πr2
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° × πR2 - θ/360° × πr2
= θ/360° × π (R2 - r2)
= 30°/360° × 22/7 [(21 cm)2 - (7 cm)2]
= 1/12 × 22/7 × (441 cm2 - 49 cm2)
= 11/42 × 392 cm2
= 308/3 cm2
☛ 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 cm2.
☛ 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.