Question

Find the measure (in degrees) of the central angle.The area of a sector is 6pi sq units. The radius is 6.The measure is ___

Answer 1

We have a circular sector, with radius 6 and an area of 6*pi square units:

We have to calculate the value of the angle.

We can use the fact that we have a fraction of the circle. We can calculate what fraction of the circle it represents by dividing the area of the sector by the area of the circle:

`(A)/(A_c)=(6\pi)/(\pi r^2)=(6\pi)/(6^2\pi)=(1)/(6)`

We know that our sector is 1/6 of the circle.

Then, the angle is 1/6 of the total angle of the circle, which, in degrees, is 360 deg.

Then, we can calculate our angle multiplying 1/6 by 360:

`\alpha=(1)/(6)\cdot360=60`

The measure is 60 degrees.