Final answer:
The length of the arc in a circle with a diameter of 24 cm and a central angle of 240° is 16π cm.
Step-by-step explanation:
In a circle, the length of an arc is given by the formula:
arc length = (central angle/360) x circumference of the circle
In this case, the central angle is 240° and the diameter of the circle is 24 cm. So, the radius of the circle is half the diameter, which is 12 cm. Therefore, the circumference of the circle is 2πr = 2π(12) cm = 24π cm.
Now, substituting the values into the formula:
arc length = (240°/360) x 24π cm = (2/3) x 24π cm = 16π cm
So, the length of the arc is 16π cm.