find the area of a sector with a central angle of 150 degree in a circle whose radius measures 12 meters
To find the area of a sector, we need to know the central angle and the radius of the circle.
In this problem, the central angle is 150 degrees and the radius is 12 meters.
We first need to find the area of the entire circle using the formula:
Area of Circle = π × radius^2
Area of Circle = π × (12)^2
Area of Circle = 144π
Next, we need to find the fraction of the circle that the sector covers. Since the central angle is 150 degrees and there are 360 degrees in a circle, the fraction of the circle covered by the sector is:
150/360 = 5/12
Finally, we can find the area of the sector by multiplying the fraction of the circle covered by the area of the whole circle:
Area of Sector = (5/12) × 144π
Simplifying this expression, we get:
Area of Sector = 60π
Therefore, the area of the sector is 60π square meters.