Question

A round table top has six equal designs as shown in the
figure if the radius of the table top is 14 cm. find the cost of
making the design with paint at the rate of Rs. 5 per cm?​

Answer 1

Number of equal designs = 6

Radius of round table cover = 14 cm

Cost of making design = ₹ 5 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°

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

Area of equilateral ΔAOB = √3/4 × (14)2 = √3/4 × 196 = 84.87 cm2

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

                                            = 1/6 × 22/7 × 14 × 14 =

102.57 cm2

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

                        =102.57 cm2 - 84.87 cm2 =17.69 cm2

Area of 6 design = 6 × 17.69 cm2 = 106.14cm2

Total cost of making design = 106.14 cm2 × ₹ 5 per cm2 = 530.7

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