Example 2 : Find the area of the segment AYB
shown in Fig. 11.6, if radius of the circle is 21 cm and
AOB = 120°.

EXERCISE 11.1
1. Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.

2. Find the area of a quadrant of a circle whose circumference is 22 cm.

3. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute
hand in 5 minutes.

4. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of
the corresponding : (i) minor segment (ii) major sector. (Use  = 3.14)

5. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:
(i) the length of the arc (ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord

6. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find
the areas of the corresponding minor and major
segments of the circle.

7. A chord of a circle of radius 12 cm subtends an
angle of 120° at the centre. Find the area of the
corresponding segment of the circle.


8. A horse is tied to a peg at one corner of a square
shaped grass field of side 15 m by means of a 5 m
long rope (see Fig. 11.8). Find
(i) the area of that part of the field in which the
horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m

9. A brooch is made with silver wire in the form
of a circle with diameter 35 mm. The wire is also
used in making 5 diameters which divide the
circle into 10 equal sectors as shown in
Fig. 11.9. Find :
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.

10. An umbrella has 8 ribs which are equally spaced
Assuming umbrella to be a flat
circle of radius 45 cm, find the area between the
two consecutive ribs of the umbrella.

11. A car has two wipers which do not overlap. Each
wiper has a blade of length 25 cm sweeping
through an angle of 115°. Find the total area
cleaned at each sweep of the blades.

12. To warn ships for underwater rocks, a lighthouse
spreads a red coloured light over a sector of
angle 80° to a distance of 16.5 km. Find the area
of the sea over which the ships are warned.

13. A round table cover has six equal designs as
shown in Fig. 11.11. If the radius of the cover is
28 cm, find the cost of making the design at the rate of Rs 0.35 per cm2
14. Tick the correct answer in the following :
Area of a sector of angle p (in degrees) of a circle
with radius R is
(A) 2 R
180
p   (B) 2 R
180
p   (C) 2 R
360
p   (D) 2 2 R