Answer to Question #188353 in Geometry for mark

Question

The radius of a circle is 5 centimeters. What is the angle measure of an arc bounding a sector with area 5​𝜋 square centimeters?

Answer 1

Given, a circle of radius (r) is 5 cm and area of sector is 11π sq. cm.

Ratio of the circle’s total area and the sector’s area.

Total Area of Circle A = π r² = π 5² = 25 π sq. cm.

Then, Sector Area = 11 π cm²/25 π cm² = 11/25

Since, the sector is 11/25 th of the circles area.

Then, the sector angle will measure 11/25 th of the circle’s circumference(c).

c = 2 π r = 2 π (5) = 10 π cm

Therefore,

Sector Arc = measure of sector angle = 11/25 (10 π) = 22π/5 radians

Thus, the angle measure of an arc bounding a sector with area 5​𝜋 square centimeters is 22π/5 radians.