To find the arc length intercepted by a 45-degree angle in a circle with a radius of 4 cm, we can use the formula for arc length, which is:
Arc Length (L) = (θ/360) × 2πr
Here, θ is the angle in degrees, and r is the radius of the circle.
Now, substituting the values into the formula:
- θ = 45 degrees
- r = 4 cm
Plugging in the values:
L = (45/360) × 2π × 4
First, simplify 45/360 to get 1/8:
L = (1/8) × 2π × 4
Now, simplifying further:
L = (1/8) × 8π = π
Thus, the arc length intercepted by a 45-degree angle in a circle with a radius of 4 cm is π cm, which is approximately 3.14 cm.