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 ✓3=1.7)


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Answer 1

Answer:

OB=OC=28cm

Area of circle= πr^2

22/7*28*28=2464

Since ABCDEF IS a hexagon

Since ∆OBC is equilateral triangle

√3/4*28*28= 339.08 cm ^2

Area of 6 triangle = 6*339.08=203.48cm^2

Area of shaded region= Area of circle -Area of 6 triangle

2464-203.48=429.52cm^2

Rate = o.35* 429.52 =150.332

Hope this is write

Answer 2

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Total number of equal designs = 6

AOB= 360°/6 = 60°

Radius of the cover = 28 cm

Cost of making design = ₹ 0.35 per cm2

Since the two arms of the triangle are the radii of the circle and thus are equal, and one angle is 60°, ΔAOB is an equilateral triangle. So, its area will be (√3/4)×a2 sq. units

Here, 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