Reema mother's is making a table cover for a round table. Reema painted a designe on it. It has six equal designs as shown in the given figure. The radius of the cover is 28 cm. ( use √3 = 1.73)
Answers
Complete Question :- Reema mother's is making a table cover for a round table. Reema painted a designe on it. It has six equal designs as shown in the given figure. 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 = 1.73) .
Solution :-
→ ∠AOB = 360°/6 = 60°
Now, in ΔAOB we have,
→ OA = OB (Radius of the circle.)
→ ∠A = ∠B (Angle opposite to equal sides are equal.)
so,
→ ∠A + ∠B + ∠O = 180°
→ 2 ∠A = 180° - 60°
→ ∠A = 120°/2
→ ∠A = 60°
then,
- ∠A = ∠B = ∠C = 60°
therefore,
→ Area of Equilateral ΔAOB = (√3/4) * (OA)² = (√3/4) * (28)² = (√3 * 7 * 28) = 1.73 * 196 = 339.08 cm²
Also,
→ Area of sector AOB = (60°/360°) * π(radius)² = (1/6) * (22/7) * (28)² = (1/3) * 11 * 4 * 28 = (1232/3) = 410.67 cm².
Hence,
→ Area of design = Area of sector AOB - Area of equilateral ΔAOB = 410.67 - 339.08 = 71.59 cm².
So,
→ Area of 6 design = 6 * 71.59 = 429.54 cm².
∴
→ Total cost of making design = 429.54 * 0.35 = Rs.150.33 (Ans.)
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