Find the length of the arc s on a circle of radius r interce

Find the length of the arc, s, on a circle of radius r intercepted by a central angle theta. Express the arc length in terms of pi. Then round your answer to two decimal places. Radius, r = 19 inches; Central angle, theta = 55degree s = inches (Simplify your answer. Type your answer in terms of pi. Use integers or fractions for any numbers in the expression.) s = inches (Type your answer rounded to two decimal places.)

Solution

The measure of the central angle tells what portion of the whole circle the sector it is. 55/360 = 11/72 of the circle.
The circumference of a whole circle is 2 pi r, but you want 11/72 of that. SO, the arc lengh is:
(11/72)(2)(pi)(19) inches

so arc length = approximately 18.2 inches