Sure, we can find this by using the arc length formula which is: (angle/360) * 2*pi*radius.
Here's a step-by-step solution:
1. Given that the radius of the circle is r = 10 cm and the central angle subtending the arc is 108 degrees.
2. The formula for the length of the arc of a circle is given by (angle/360) * 2 * pi * r, where "angle" is the measure of the arc's central angle in degrees, "pi" is a constant approximately equal to 3.14159, and "r" is the radius of the circle.
3. By substituting in the given values into the formula, we have:
(108/360) * 2 * pi * 10.
4. Next, simplify the expression. 108/360 reduces to 0.3.
5. Then, calculate 0.3 * 2 * pi * 10 which is approximately equal to 18.85 cm.
Therefore, the length of the arc subtended by a central angle of 108° in a circle with a radius of 10 cm is about 18.85 cm.