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.

2 answers

Question:

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: The ratio of the measure of the central angle to the entire circle measure is 1:2.Explanation:The measure of MNL angle = [tex]\pi \text{ radians}[/tex]The measure of the entire circle is = [tex]2\pi \text{ radians}[/tex]The ratio of the measure of the central angle to the entire circle measure is :=[tex]=\frac{Angle MNL}{\text{Angle of entire circle}}=\frac{\pi \text{ radians}}{2\pi \text{ radians}}=\frac{1}{2}[/tex]Hence, the ratio of the measure of the central angle to the entire circle measure is 1:2.Area of circle [tex]=\pi r^2=\pi (unit)^2[/tex]Area of sector = ratio of angle subtended by the sector to circle [tex]\times [/tex] area of circle Area of sector =[tex]\frac{1}{2}\times \pi =\frac{1}{2}\pi (unit)^2[/tex]

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