a round table cover has six equal design as shown in figure 12.14 if the radius of the cover is 28 cm find the cost of making the design at the rate of rupees 0.35% square use root 3 equal to 1.7??
Answers
Answer:
Total cost of making design = Rs 162.66 rupees
Step-by-step explanation:
Given,
- Number of equal designs = 6
- Radius of round table cover = 28 cm
- Cost of making design = Rs 0.5 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 × (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 = Rs 162.66
∴ Total cost of making design = Rs 162.66 rupees
Answer:
Step-by-step explanation:
Answer:
Good night
Step-by-step explanation:
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 × (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
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