Question

Circle N is shown. Line segment M L is a diameter. The length of N L is 6. Everything above angle M N L is shaded. The measure of central angle MNL is π radians, and the measure of the entire circle is 2π radians. The ratio of the measure of the central angle to the entire circle measure is . The area of the entire circle is π units2. The area of the sector is π units2.

Answer 1

The ratio of the measure of the central angle to the entire circle measure
`=(1)/(2)`

The area of the entire circle
`=36\pi$ units^2.`

The area of the sector
`=18\pi $ units^2`

Explanation:

MNL is a diameter of the circle N

Radius, NL =6

• The measure of central angle MNL = π radians
• The measure of the entire circle = 2π radians.

The ratio of the measure of the central angle to the entire circle measure

`=(\pi)/(2\pi)\\\\ =(1)/(2)`

Area of a circle
`=\pi r^2`

The area of the entire circle

`= \pi * 6^2 \\=36\pi$ units^2.`

Therefore, the area of the sector

`=(1)/(2) * 36\pi\\=18\pi $ units^2`