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13.  A round table cover has six equal designs as shown in Fig. . 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. (Use \sqrt3 = 1.7)

                                          

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The angle of each of the six sectors is 60o at the centre.                                                       \left ( \because \frac{360^{\circ}}{6}\ =\ 60^{\circ} \right )

Area of the sector is given by:- 

                                                      Area\ =\ \frac{\Theta}{360^{\circ}}\ \times \pi r^2

or                                                               =\ \frac{60^{\circ}}{360^{\circ}}\ \times \pi \times 78^2

or                                                               =\ 410.66\ cm^2

And the area of the equilateral triangle associated with segment:- 

                                                                  =\ \frac{\sqrt{3}}{4}\times a^2

or                                                              =\ \frac{\sqrt{3}}{4}\times 28^2\ =\ 333.2\ cm^2

Hence the area of segment is :          =\ 410.66\ -\ 333.2\ =\ 77.46\ cm^2

Thus the total area of design is :         =\6\times 77.46\ =\ 464.76\ cm^2

So, the total cost for the design is:-      =\ 0.35\times 464.76\ =\ Rs. 162.66

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Devendra Khairwa

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