To calculate the arc length intercepted by a given angle in a circle, we can use the formula:
Arc Length (L) = (θ / 360) x 2πr
Where:
- L = Arc Length
- θ = Angle in degrees
- r = Radius of the circle
Given:
- Radius (r) = 4 cm
- Angle (θ) = 45 degrees
Now, let’s plug in the values:
L = (45 / 360) x 2π x 4
Calculating the fraction:
45 / 360 = 1/8
Now substituting the fraction back into the formula:
L = (1/8) x 2π x 4
Next, compute the multiplication:
L = (1/8) x 8π
This simplifies to:
L = π
Now, substituting the approximate value of π:
L ≈ 3.14 cm
Thus, the length of the arc intercepted by a 45-degree angle in a circle with a radius of 4 cm is approximately 3.14 cm.