A round table top has six equal designs as shown in the figure. If the radius of the table top is 14 cm., find the cost of making the designs with paint at the rate of ₹5 per cm². (use √3 = 1.732)
Answers
Answer:
536.90
Step-by-step explanation:
Considering segment APB where chord AB is a side of the hexagon.
Each chord will substitute 360/6 = 60 at the center of the circle.
In ΔOAB,
∠OAB = ∠OBA (OA = OB)
∠AOB = 60°
∠OBA+ ∠OAB + ∠AOB = 180°
2∠OAB = 180° − 60° = 120°
∠OAB = 60°
Therefore, ΔOAB is an equilateral triangle.
Area of triangle = √3/4 side²
= √3/4 (14)²
= 49√3
= 49 × 1.732 = 84.77
Area of sector OAPB = 60/360 × πr²
= 1/6 × 22/7 x 14 × 14
= 308/3 cm²
Area of segment APB = Area of sector OAPB − Area of ΔOAB
= 308/3 - 84.77
Area of design = 6 × 308/3 - 84.77
= 107.38
Cost of making 1 cm² designs = Rs 5
Cost of making 107.38 cm² designs = 107.38 × 5 = 536.9
Therefore, the cost of making such designs is Rs 536.90
Answer:
Considering segment APB where chord AB is a side of the hexagon.
Each chord will substitute 360/6 = 60 at the center of the circle.
In ΔOAB,
∠OAB = ∠OBA (OA = OB)
∠AOB = 60°
∠OBA+ ∠OAB + ∠AOB = 180°
2∠OAB = 180° − 60° = 120°
∠OAB = 60°
Therefore, ΔOAB is an equilateral triangle.
Area of triangle = √3/4 side²
= √3/4 (14)²
= 49√3
= 49 × 1.732 = 84.77
Area of sector OAPB = 60/360 × πr²
= 1/6 × 22/7 x 14 × 14
= 308/3 cm²
Area of segment APB = Area of sector OAPB − Area of ΔOAB
= 308/3 - 84.77
Area of design = 6 × 308/3 - 84.77
= 107.38
Cost of making 1 cm² designs = Rs 5
Cost of making 107.38 cm² designs = 107.38 × 5 = 536.9
Therefore, the cost of making such designs is Rs 536.90
Step-by-step explanation: