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 cm^{2}. (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 hexagon.

And,

Each chord will substitute = 60^{o} 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 cm^{2}

Area of sector OAPB = * r^{2}

= * * 28 * 28

= cm^{2}

Now,

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

= ( - 333.2) cm^{2}

Area of design = 6 * ( - 333.2)

= 2464 – 1992.2

= 464.8 cm^{2}

Cost of making 1 cm^{2} designs = Rs 0.35

Cost of making 464.76 cm^{2} designs = 464.8 * 0.35

= Rs 162.68

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

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