Question

The area of the sector of a circle with a radius of 8 centimeters is 125.6 square centimeters. The estimated value of is 3.14.

The measure of the angle of the sector is

Answer 1

225º

Explanation:

Answer 2

225º or 3.926991 radians

Explanation:

The area of the complete circle would be π×radius²: 3.14×8²=200.96

The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.

`(125.6)/(200.96)`=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).

There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.

We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.