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)

Question

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)

Philoid · Accepted Answer

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 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 – 1992.2

= 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

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)

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)