Given:
Given that the circle has a center O.
The radius of the circle is 8 m.
The measure of ∠AOB is 120°
We need to determine the area of the shaded region and the length of the arc ADB.
Measure of ∠ADB:
The measure of ∠ADB is given by
[tex]\angle ADB=360^{\circ}-\angle AOB[/tex]
Substituting the values, we have;
[tex]\angle ADB=360^{\circ}-120^{\circ}[/tex]
[tex]\angle ADB=240^{\circ}[/tex]
Thus, the measure of ∠ADB is 240°
Area of the shaded region:
The area of the shaded region can be determined using the formula,
[tex]A=(\frac{\theta}{360}) \pi r^2[/tex]
[tex]A=(\frac{240}{360}) \pi (8)^2[/tex]
[tex]A=(\frac{240}{360}) \pi (64)[/tex]
[tex]A=42.67 \pi \ m^2[/tex]
Thus, the area of the shaded region is 42.67π m²
Length of arc ADB:
The length of arc ADB can be determined using the formula,
[tex]Arc \ length=(\frac{\theta}{360})2 \pi r[/tex]
[tex]Arc \ length=(\frac{240}{360})2 \pi (8)[/tex]
[tex]Arc \ length=10.67 \pi \ m[/tex]
Thus, the arc length of ADB is 10.67π m
