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

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