To find the exact length of arc ABC, we can use the formula for the length of an arc, which is given by:
Arc Length = (θ / 360) * 2πr
Where:
- θ is the angle in degrees (in this case, 324 degrees),
- r is the radius of the circle (40 centimeters),
- π is approximately 3.14 or can be used as the constant π for exact calculations.
Now, substituting the values into the formula:
Arc Length = (324 / 360) * 2π * 40
First, we simplify:
Arc Length = (0.9) * 2π * 40
Arc Length = 1.8π * 40
Arc Length = 72π
If we use the approximate value of π (3.14), we get:
Arc Length ≈ 72 * 3.14 ≈ 226.08 centimeters
Thus, the exact length of arc ABC is 72π centimeters, and approximately it is 226.08 centimeters.