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25/06/2021 1:23 pm
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A round table cover has six equal designs as shown in Figure. 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 √3 = 1.7)
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25/06/2021 1:33 pm
Total number of equal designs = 6
AOB = 360°/6 = 60°
Radius of the cover = 28 cm
Cost of making design = Rs 0.35 per cm2
So, its area will be (√3/4)×a2 sq. units
a = OA
∴ Area of equilateral ΔAOB = (√3/4)×282
= 333.2 cm2
Area of sector ACB = (60°/360°) × πr2 cm2
= 410.66 cm2
So, area of a single design = area of sector ACB – area of ΔAOB
= 410.66 cm2 – 333.2 cm2
= 77.46 cm2
∴ Area of 6 designs = 6×77.46 cm2 = 464.76 cm2
So, total cost of making design = 464.76 cm2 × Rs.0.35 per cm2
= Rs. 162.66