Question

Find the measure of the central angle of a sector if its area is 5 pi and the radius is 6

Answer 1

For this case we use the following formula
 Area of Sector = Area * radians of sector / 2 * pi radians
 Where,
 Area: it is the area of the complete circle.
 We have then:
 Area = pi * r ^ 2
 Area = pi * (6) ^ 2
 Area = 36pi
 Substituting values:
 5pi = 36pi * radians of sector / 2 * pi
 Clearing:
 radians of sector = ((5pi) * (2pi)) / (36pi)
 radians of sector = (10pi ^ 2) / (36pi)
 radians of sector = (10pi) / (36)
 radians of sector = (10/36) pi
 radians of sector = (5/18) pi
 in degrees:
 (5/18) pi * (180 / pi) = 50 degrees
 Answer:
 The measure of the central angle is:
 50 degrees