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11. 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.

Here, we have
r = 15 cm, ө = 60°
Let OACBO be the given sector and OAB is a triangle. Then

Here, we haver = 15 cm, ө = 60°Let OACBO be the given sector and OA
(i) Area of the sector (OACBO)

$equals space πr squared cross times straight theta over 360 space equals space open parentheses 3.14 space straight x space 15 space straight x space 15 space straight x space 60 over 360 close parentheses space cm squared equals space 117.75 space space cm squared$

(ii) Area of the triangle (AOB)

$equals space 1 half straight r squared space sin space straight theta equals space 1 half straight x space 15 space straight x space 15 space straight x space fraction numerator square root of 3 over denominator 2 end fraction equals space space fraction numerator 15 straight x 15 straight x 1.73 over denominator 4 end fraction equals 97.313 space cm squared$

Now,
Area of Minor segment (ACBA)
= Area of sector (OACBO) - Area of triangle (AOB)
= (117.75 - 97.313) cm²= 20.437 cm²and Area of Major segment (ABDA)
= Area of circle-Area of Minor segment
= (πr³ - 20.437) cm²= (3.14 × 15 × 15 - 20.437) cm²= (706.5 - 20.437) cm²= 686.063 cm².

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Long Answer Type

12. 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.

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13.

A horse tied to a corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). 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 5m.

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Short Answer Type

14.

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 divides the circle into 10 equal sectors as shown in figure. Find
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.

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15. An umbrella has 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.

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16. 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.

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17. To throws ships of underwater rocks, a lighthouse throws 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. (Use π = 3.14).

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18. A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs. 0.35 per cm².