Final answer:
To find the cost of the designing, we first need to determine the area of the portion in the form of a rectangular hexagon inscribed in the round table. Next, we find the area of the remaining portion of the table top, which is represented by a circle. Finally, we calculate the cost of the designing by multiplying the area of the designs by the rate of rupees 8 per 15cm².
Step-by-step explanation:
To find the cost of the designing, we first need to determine the area of the portion in the form of a rectangular hexagon. The hexagon is inscribed in a round table with a diameter of 12 cm, so the side length of the hexagon is equal to the radius of the table, which is 6 cm. The area of a hexagon can be calculated using the formula A = (3√3 / 2) × s², where s is the length of a side. Substituting s = 6 cm into the formula, we get:
A = (3√3 / 2) × 6² = 54√3 cm²
Next, we need to find the area of the remaining portion of the table top. Since the table is round, the remaining portion can be represented by a circle with a radius of 6 cm. The area of a circle can be calculated using the formula A = πr², where r is the radius. Substituting r = 6 cm into the formula, we get:
A = π × 6² = 36π cm²
Now, we can find the area of the designs by subtracting the area of the hexagon from the area of the circle:
Designs area = Area of circle - Area of hexagon = 36π cm² - 54√3 cm²
Finally, we can find the cost of the designing by multiplying the area of the designs by the rate of rupees 8 per 15cm²:
Cost of designing = (Designs area / 15cm²) × 8