Final answer:
The arc length of an astroid is found using a specific formula, not provided in the options, which is Arc Length = 6a. The referenced formulas and concepts apply to circular paths, where arc length is calculated as 2πr for a full revolution, and not to an astroid curve.
Step-by-step explanation:
To find the arc length of an astroid, one must understand the properties of the curve. However, the information provided and the options suggested relate to a circular path rather than that of an astroid, which has a different form. The correct formula to calculate the arc length of an entire astroid, given its semi-major axis 'a,' is actually Arc Length = 6a. This is a special property of the astroid curve, and it's derived from the parametric equations and integral calculus that define the curve.
For a circular path, we use Δθ = s/r, where 's' is the arc length, 'r' is the radius, and Δθ is the angle in radians. The arc length is directly proportional to the radius and the angle of rotation. For a complete revolution of a circle, the rotation angle is Δθ = 2π, therefore the arc length would be 2πr, which is the circumference of the circle.