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
*0.35 per cm. (Use 13 =1.7)​

Answer 1

Number of equal designs = 6

The radius of round table cover = 28 cm

Cost of making design = 0.35 per cm2

∠O = 360°/6 = 60°

ΔAOB is isosceles as two sides are equal. (Radius of the circle)

∴ ∠A = ∠B

Sum of all angles of triangle = 180°

∠A + ∠B + ∠O = 180°

⇒ 2 ∠A = 180° – 60°

⇒ ∠A = 120°/2

⇒ ∠A = 60°

∠A = ∠B = ∠C = 60°

Area of equilateral ΔAOB = √3/4 × (OA)2 = √3/4 × 282 = 333.2 cm2

Area of sector ACB = (60°/360°) × π r2 cm2 = 1/6 × 22/7 × 28 × 28 = 410.66 cm2

Area of design = Area of sector ACB – Area of equilateral ΔAOB

= 410.66 cm2 – 333.2 cm2 = 77.46 cm2

Area of 6 design = 6 × 77.46 cm2 = 464.76 cm2

Total cost of making design = 464.76 cm2 × 0.35 per cm2 = 162.66

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Answer 2

Answer:

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Sum of all angles of triangle = 180°

∠A + ∠B + ∠O = 180°

⇒ 2 ∠A = 180° - 60°

⇒ ∠A = 120°/2

⇒ ∠A = 60°

Triangle is equilateral as ∠A = ∠B = ∠C = 60°

Area of equilateral ΔAOB = √3/4 × (OA)2 = √3/4 × 282 = 333.2 cm2

Area of sector ACB = (60°/360°) × π r2 cm2

                                           = 1/6 × 22/7 × 28 × 28 = 410.66 cm2

Area of design = Area of sector ACB - Area of equilateral ΔAOB

                       = 410.66 cm2 - 333.2 cm2 = 77.46 cm2

Area of 6 design = 6 × 77.46 cm2 = 464.76 cm2

Total cost of making design = 464.76 cm2 × ₹ 0.35 per cm2 = ₹ 162.66  

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