Question

The diameter of a circle is 8 feet. What is the angle measure of an arc a feet long?

Give the exact answer in simplest form.
20 points​

Answer 1

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