A round table cover has 6 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 square. (Use root 3 = 1.7
Answers
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
Answer:
mber 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