A string is wound symmetrically around a circular rod............................What is the length of the string?

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A string is wound symmetrically around a circular rod.
The string goes exactly 4 times around the rod.
The rod has a circumference of 4 and a length of 12.
What is the length of the string?

In a semicircle, the circular segment ADB is folded along AB to make the circular segment ATB. The point T is tangent to the diameter and divides the diameter into lengths of 4 and 2.
What is the length of AB?

A circular sector with central angle equal to 120 as shown in figure. We want to place a square symmetrically in it as shown. If the radius of the circular sector is 100 units, what is the side length of the square ?

A circular sector can be folded into a cone by joining its two radii.
For a circular sector with a radius equal to 1, what is the maximum volume of the cone? If the circular sector has a central angle θ, what is the value of θ at the maximum volume?