# 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. (Use = 1.7)

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

Let us take segment APB.

Chord AB is a side of the regular hexagon.

And,

Each chord will substitute = 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°

Hence,

ΔOAB is an equilateral triangle.

Area of ΔOAB = (Side)2

=  × (28)2

= 196

= 333.2 cm2

Area of sector OAPB = × r2

= × × 28 × 28

= cm2

Now,

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

= ( - 333.2) cm2

Area of design = 6 × ( - 333.2)

= 2464 – 1999.2

= 464.8 cm2

Cost of making 1 cm2 designs = Rs 0.35

Cost of making 464.76 cm2 designs = 464.8 × 0.35

= Rs 162.68

Hence, the cost of making such designs would be Rs 162.68.

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