In a circle whose radius is 6, find the area of a sector, in terms of pi, whose center angle contains 30 degrees
As = ((pi/6)/2pi)*pi *6^2
As = 1/6 * 1/2 * 36pi = 3pi.
To find the area of a sector in a circle, you need to know two things:
1. The central angle of the sector.
2. The radius of the circle.
In this case, the central angle of the sector is given to be 30 degrees, and the radius of the circle is 6.
The formula to calculate the area of a sector is:
Area = (θ/360) * π * r^2
Where:
- θ is the central angle in degrees
- π is a constant approximately equal to 3.14159
- r is the radius of the circle
So, plugging in the given values:
θ = 30 degrees
r = 6
Area = (30/360) * π * (6^2)
Area = (1/12) * π * 36
Area = (π/12) * 36
Area = 3π square units
Therefore, the area of the sector is 3π square units.