A round table cover has six equal designs as shown in Fig. 12.14
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    Areas Related to Circles

    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

    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.

    Here, we have
    r = 28 cm  and  straight theta space equals space 360 over 6 equals 60 degree

    Here, we haver = 28 cm  and  Now,  Area of Minor sector       

    Now,  Area of Minor sector

             πr squared cross times straight theta over 360 equals space open parentheses 22 over 7 straight x 28 space straight x space 28 space straight x space 60 over 360 close parentheses space cm squared equals space 1232 over 3 space cm squared equals 410.67 space cm squared OA space space equals space OB space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket Radii space of space the space same space circles right square bracket OM space equals space OM space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket Common right square bracket therefore space increment space OMA space equals space increment space OMB space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket Using space RHS space congruent space condition right square bracket therefore space space space AM space equals space BM space space space space space space space left square bracket space By space CPCT right square bracket rightwards double arrow space space AM space space equals space BM space equals space 1 half space AB and space space angle AOM space space equals space angle BOM space equals space 1 half angle AOB space space space space space space space space equals space 1 half left parenthesis 60 degree right parenthesis space equals space 30 degree
    In right triangle OMA, we have

    cos space 30 degree space equals space OM over OA rightwards double arrow space space fraction numerator square root of 3 over denominator 2 end fraction equals OM over 28 rightwards double arrow space space space OM space equals space 14 square root of 3 space cm sin space 30 degree space equals space AM over OA rightwards double arrow space space 1 half space equals space AM over 28 rightwards double arrow space space space AM space equals space 14 space cm rightwards double arrow space space 2 AM space equals space 28 space cm rightwards double arrow space space space AB space equals space 28 space cm therefore space space Area space of space increment space AOB space equals space 1 half cross times AB cross times OM space space space space space space space space space space space space space space space space space space space space space equals space 1 half cross times 28 cross times 14 square root of 3 space space space space space space space space space space space space space space space space space space space space space equals space 196 square root of 3 space space space cm squared space space space space space space space space space space space space space space space space space space space space space equals space 196 space straight x space 1.7 space cm squared space space space space space space space space space space space space space space space space space space space space space space equals space 333.2 space cm squared space space space space space space space space space space space space
    therefore Area of one design = 77.47 cm2 
    therefore space spaceArea of six design = 77.47 x 6
                                    = 464.82 cm2 
    therefore space space Cost space of space making space the space designs space at space the space rate space of space Rs. space 0.35 space per space cm squared

                               = 464.82 x 0.35
                               = Rs. 162.68
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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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