How do you calculate the area of a sector of a circle with a radius of 8 inches and an angle of 45 degrees?

To find the area of a sector of a circle, you can use the formula:

Area = (θ / 360) × π × r²

Where:

• θ is the angle of the sector in degrees
• r is the radius of the circle

In this case:

• r = 8 inches
• θ = 45 degrees

Now, plug these values into the formula:

Area = (45 / 360) × π × (8)²

Calculating step by step:

1. Calculate (8)²:
2. (8)² = 64
3. Now plug this value into the formula:
4. Area = (45 / 360) × π × 64
5. Simplify (45 / 360):
6. (45 / 360) = 1 / 8

Now the area becomes:

Area = (1 / 8) × π × 64

Calculate:

Area = 8π

So, the area of the sector is:

Area ≈ 25.13 square inches

Thus, we find that the area of the sector of a circle with a radius of 8 inches and an angle of 45 degrees is approximately 25.13 square inches.