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A round table cover has six equal designs as shown in figure. 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 √3 = 1.7]

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It can be observed that these designs are segments of the circle.

Consider segment APB. Chord AB is a side of the hexagon. Each chord will substitute 360o/6 = 60o at the centre of the circle.

In ΔOAB,

 ∠OAB = ∠OBA (As OA = OB)

∠AOB = 60°

∠OAB + ∠OBA + ∠AOB = 180°

2∠OAB = 180° − 60° = 120°

∠OAB = 60°

Therefore, ΔOAB is an equilateral triangle.

Area of ΔOAB =

√3/4 x (28)2=196√3

=196 x 1.7=333.2 cm2

Area of sector OAPB = 

= 1/6 x 22/7 x 28 x 28 

=1232/3 cm2

Area of segment APB = Area of sector OAPB − Area of ΔOAB

Therefore area of designs = 

=(2464-1999.2)cm2

= 464.8cm2

Cost of making 1 cm2 designs = Rs 0.35

Cost of making 464.76 cm2 designs = 464.8 x 0.35 =RS 162.68

Therefore, the cost of making such designs is Rs 162.68.

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