To find the area of a sector of a circle, you can use the formula:
Area of the sector = (θ / 360) * π * r²
Here, θ is the angle in degrees and r is the radius.
In this case, the radius (r) is 8 inches and the angle (θ) is 45 degrees. Plugging these values into the formula gives:
Area = (45 / 360) * π * (8)²
Calculating this step by step:
- First, calculate (8)², which is 64.
- Then, substitute that into the formula: Area = (45 / 360) * π * 64.
- Next, simplify (45 / 360) to (1 / 8), so now it reads: Area = (1 / 8) * π * 64.
- When you multiply, you get Area = 8π.
Therefore, the area of the sector is 8π square inches. If you want a numerical approximation, you can use 3.14 for π, which would give you about 25.12 square inches.