This problem is actually to calculate the sum of three circumscribed circles, three tangents and three arc lengths.

The length of the outer common tangent of every two circles is equal to the sum of the two radii, which is equal to the diameter.

The circumference of each arc is equal to one third of the circumference of a circle, so three segments are equal to the circumference of a circle.

So the rope length = 10×3+π× 10.

= 10×(3+π)

≈ 10×6. 14

≈ 61.4cm.

Answer: At least 6 1.4cm long rope is required.