# A circle with a radius of 15mm, divided into three arcs of equal length. Find the length of the filled arc.

If we understand that, according to the problem statement, one arc is painted over, the solution is as follows.

The length of a circular arc is determined by the formula: p = (π * R * n) / 180, where

p is the length of the arc;

π is pi, approximately equal to 3.14;

n is the size of the central angle of the arc in degrees.

The center angle is the angle formed by two radii with the vertex at the center of the circle.

If the circle is divided into three equal arcs, then they rest on 3 equal central angles. The magnitude of each of them is 360/3 = 120 degrees.

p = (3.14 * 15 * 120) / 180 = (3.14 * 15 * 2) / 3 = 3.14 * 10 = 31.4 mm.

If 2 arcs are painted over: 2 * 31.4 = 62.8 mm.

If 3 arcs are painted over, this is already a circle: 3 * 31.4 = 94.2 mm. Or according to the formula for the circumference L = 2 * π * R = 2 * 3.14 * 15 = 94.2 mm.