A central angle in a circle with a diameter of 9 meters measures radians. 7/18 Find the length
of the arc intercepted by this angle
We can use the formula for the length of an arc of a circle:
length of arc = radius x angle measure
Since the diameter of the circle is 9 meters, the radius is half of that, or 4.5 meters. The angle measure is given as 7/18 radians. Therefore, the length of the arc intercepted by this angle is:
length of arc = 4.5 x (7/18) = 1.75 meters (rounded to two decimal places)
To find the length of the arc intercepted by a central angle in a circle, you can use the formula:
Arc Length = (Central Angle / 2π) * Circumference
The circumference of a circle with a diameter of 9 meters can be calculated as:
Circumference = π * Diameter
Plugging in the values, we can calculate the circumference:
Circumference = π * 9 meters = 9π 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 / 2π) * 9π 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.