Answer
The provided statement is false.
Work Step by Step
If $r$ is the radius of a circle and $\theta $ is the angle subtended at the center in radians and is non-negative, then the length of the arc $s$ is given by
$s=r\theta $
However, in the provided statement, the angle $\theta $ is given in degrees and $s$ is calculated by that value only.
Therefore, the statement “If $r=10$ centimeters and $\theta =20{}^\circ $ , then $s=10\cdot 20=200$ centimeters” is false.
