Answer:
Given: circle
diameter = 10 cm => radius (R) = 5 cm
Find: measure of angle bounding sector = 11 π sq. cm.
Plan: determine what part of the circle’s total area equals the sector’s area.
Total Area of Circle A = π R^2 = π 5^2 = 25 π sq. cm.
Therefore: Sector Area = 11 π cm^2/25 π cm^2 = 11/25
Since the sector is 11/25 th of the circles area, the sector angle will measure 11/25 th of the circle’s circumference. They are proportional.
C = 2 π R = 2 π (5) = 10 π cm
Sector Arc = measure of sector angle = 11/25 (10 π) =
22π/5 radians
Answer: Sector Arc = 22π/5 Radians