A round table cover has six equal designs as shown in fig. 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. (Use √3 = 1.7)

Let the radius of the round table cover be r = 28 cm.
The table cover has 6 equal designs. Each design is a sector of the circle.
The angle subtended by each sector at the center is 360°/6 = 60°.
The area of one sector is (θ/360°) * πr² where θ is the central angle.
Area of one sector = (60°/360°) * π * (28)² = (1/6) * π * 784 cm²
Since we are given to use √3 = 1.7, we can approximate π as 3.14 (or a more accurate approximation if needed).
Area of one sector ≈ (1/6) * 3.14 * 784 ≈ 410.61 cm²
The perimeter of one sector consists of two radii and the arc length.
Arc length = (θ/360°) * 2πr = (60°/360°) * 2 * π * 28 = (1/6) * 2 * π * 28 = (28/3)π cm
Perimeter of one sector = 2r + (28/3)π = 2(28) + (28/3)π ≈ 56 + (28/3) * 3.14 ≈ 56 + 29.306 ≈ 85.306 cm
There are 6 such sectors, so the total perimeter of all sectors is approximately 6 * 85.306 cm ≈ 511.836 cm
However, the question asks for the cost of making the designs, implying we need the total length of the design borders.
Since each sector has two radii and an arc, we calculate the perimeter of a sector as:
Perimeter = 2r + arc length = 2(28) + (60/360) * 2π(28) = 56 + (1/3)π(28) ≈ 56 + 29.32 = 85.32 cm
Total perimeter of designs = 6 * 85.32 cm ≈ 511.92 cm
Cost of making the designs = total perimeter * cost per cm = 511.92 cm * Rs. 0.35/cm ≈ Rs. 179.17
Therefore, the approximate cost of making the designs is Rs. 179.17