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  • 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 cm 2 . (Use root 3 = 1.7)

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 )

The area of the sector is given by:- 

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

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

=\ 410.66\ cm^2

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

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

=\ \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

Posted by

Devendra Khairwa

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