To find the length of the arc intercepted by a central angle in a circle, you can use the formula:
Arc Length = (Central Angle / 2ฯ) * Circumference
The circumference of a circle with a diameter of 9 meters can be calculated as:
Circumference = ฯ * Diameter
Plugging in the values, we can calculate the circumference:
Circumference = ฯ * 9 meters = 9ฯ meters
Now, we can substitute the given central angle, which measures 7/18 radians, into the formula to find the arc length:
Arc Length = (7/18 / 2ฯ) * 9ฯ meters
Simplifying:
Arc Length = (7/18 / 2) * 9 meters
Arc Length = (7/18 * 9) / 2 meters
Arc Length = (63/18) / 2 meters
Simplifying the fraction:
Arc Length = 3.5 meters
Therefore, the length of the arc intercepted by the central angle is 3.5 meters.