Find the arc length of a central angle of 330 in a circle whose radius is 18 inches
work show would be appreciated
Recall that s = rθ (θ in radians). So,
330/360 * 2π * 18
To find the arc length of a central angle, you need to use the formula:
Arc Length = (Central Angle / 360) * (2 * π * radius)
Where:
- Central Angle is the measure of the central angle in degrees
- Radius is the length of the radius of the circle
In this case, the central angle is 330 degrees and the radius is 18 inches. Let's substitute these values into the formula:
Arc Length = (330/360) * (2 * π * 18)
First, simplify the fraction:
Arc Length = (11/12) * (2 * π * 18)
Next, calculate the expression inside the parentheses:
Arc Length = (11/12) * (36π)
Finally, multiply and simplify the expression:
Arc Length = 33π inches
Therefore, the arc length of the central angle of 330 degrees in a circle with a radius of 18 inches is 33π inches.