To find the length of the minor arc in a circle with a circumference of \(20\pi\) and a central angle of \(90\) degrees, we can use the following steps:
-
Determine the fraction of the circle represented by the central angle: The full circle is \(360\) degrees. Therefore, the fraction of the circle for the \(90\) degrees angle is: \[ \text{Fraction} = \frac{90}{360} = \frac{1}{4} \]
-
Calculate the length of the minor arc: The length of the arc can be found by multiplying the fraction of the circle by the total circumference. Thus, the length of the minor arc \(L\) is: \[ L = \text{Fraction} \times \text{Circumference} = \frac{1}{4} \times 20\pi = 5\pi \]
Therefore, the length of the minor arc is \(5\pi\).