To find the length of an arc, you can use the formula:
Arc Length = (θ / 360) × 2πr
Where:
- θ is the angle in degrees (in this case, 40°)
- r is the radius of the circle (in this case, 8 inches)
Now, substituting the values into the formula:
Arc Length = (40 / 360) × 2π × 8
First, simplify (40 / 360):
(40 / 360) = 1 / 9
Now plug that back into the arc length formula:
Arc Length = (1 / 9) × 2π × 8
To calculate 2π × 8:
2π × 8 = 16π
Putting it all together:
Arc Length = (1 / 9) × 16π
Arc Length = 16π / 9
Now, if you want a numerical approximation, using π ≈ 3.14:
Arc Length ≈ (16 × 3.14) / 9
Arc Length ≈ 50.24 / 9
Arc Length ≈ 5.58 inches
Therefore, the length of the arc of 40° in a circle with an 8 inch radius is approximately 5.58 inches.