Final answer:
The exact length of Arc AB in Circle E with a radius of 40 cm and an arc angle of 324 degrees is 144π centimeters. When calculated, it is approximately 452.39 cm, which shows that the given option of 360 cm is incorrect.
Step-by-step explanation:
The question pertains to finding the length of an arc on a circle with a given radius and angle. We are given that Circle E has a radius (r) of 40 centimeters and an arc, Arc AB, measures 324 degrees. To calculate the length of Arc AB, we use the formula that relates arc length to circumference and angle:
Arc Length (s) = (Θ/360) × 2πr
Here, Θ is the central angle in degrees, 2πr is the circumference of the circle, and s is the arc length.
For Circle E, the angle Θ is 324 degrees and the radius is 40 cm. Substituting these values into the formula, we get:
s = (324/360) × 2π(40)
s = (9/10) × 2π(40)
s = 144π centimeters
As π (pi) approximately equals 3.14159, the exact length of Arc AB is 144π centimeters, or when calculated, around 452.39 centimeters, which does not match any of the given options. Therefore, the provided answer of 360 cm is incorrect.