To find the area of a sector of a circle, we can use the following formulas:
1. The formula for the arc length (
L) of a sector is:
L = r × θ
Where:
- L is the arc length,
- r is the radius of the circle,
- θ is the angle in radians.
2. The area (
A) of a sector of a circle can be calculated using the formula:
A = (θ / 2) × r²
Given:
- Radius (r) = 18
- Arc Length (L) = 6π
Now, we can find the angle θ using the arc length formula:
6π = 18 × θ
From this, we can solve for θ:
θ = 6π / 18
Which simplifies to:
θ = π / 3
Now that we have θ, we can substitute it into the area formula:
A = (π / 3) / 2 × 18²
Calculating the area, we have:
A = (π / 6) × 324
Which simplifies to:
A = 54π
Thus, the area of the sector of the circle is 54π square units.