A brooch is made with silver wire in the form of a circle with d

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 Multiple Choice QuestionsShort Answer Type

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.
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 Multiple Choice QuestionsLong 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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 Multiple Choice QuestionsShort Answer Type

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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.




(i) Total length of the silver wire required = circumference of the circle + length of 5 diameters which divide the circle into 10 equal sectors

equals space 2 πr space space plus space 5 space straight x space 2 straight r
equals space open parentheses 2 cross times 22 over 7 cross times 35 over 2 plus 5 cross times 2 35 over 2 close parentheses space mm
equals space left parenthesis 110 space plus 175 right parenthesis space mm
equals space 285 space mm

(ii) The area of each sector of the brooch

equals 1 over 10 cross times πr squared
equals space space open parentheses 1 over 10 cross times 22 over 7 cross times 35 over 2 cross times 35 over 2 close parentheses space mm squared
equals space fraction numerator 11 cross times 35 over denominator 4 end fraction equals 385 over 4 mm squared
equals space 96.25 space mm squared

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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.


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19. Tick the correct answer in the following: Area of a sector of angle p (in degrees) of a circle with radius R is

bold left parenthesis bold A bold right parenthesis bold space bold space bold P over bold 180 bold x bold 2 bold πR bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold left parenthesis bold B bold right parenthesis bold space bold P over bold 180 bold cross times bold πR to the power of bold 2
bold left parenthesis bold C bold right parenthesis bold space bold space bold space bold P over bold 360 bold cross times bold 2 bold πR bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold left parenthesis bold D bold right parenthesis bold space bold P over bold 720 bold cross times bold space bold 2 bold πR to the power of bold 2
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20. Find the area of the shaded region, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.  


Fig. 12.19.
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