Since the radius of this circle is 8 inches, the area of a sector bounded by a 255° arc is 142.35 square inches.
In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:
Area of sector = π
× θ/360
Where:
- r represents the radius of a circle.
- θ represents the central angle.
Note: The measure of an intercepted arc is equal to the central angle of a circle.
θ = 360 - 105
θ = 255°
By substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = π
× θ/360
Area of sector = 3.14 ×
× 255/360
Area of sector = 3.14 × 64 × 17/24
Area of sector = 3.14 × 8/3 × 17
Area of sector = 142.3467 ≈ 142.35 square inches.