Find the arc length, of a 130 degree arc, in a circle with a diameter of 7.2 inches. Round your answer to the nearest thousandth
130/360 is the fraction of the whole circumference of length pi D
(130/360) * pi * (7.2)
To find the arc length of a circle, you can use the formula:
Arc Length = (angle/360) * (2 * π * radius)
First, we need to calculate the radius of the circle. We are given the diameter of 7.2 inches, which is twice the radius. So, we can divide the diameter by 2 to find the radius:
radius = 7.2 inches / 2 = 3.6 inches
Next, we can substitute the values into the formula:
Arc Length = (130/360) * (2 * π * 3.6 inches)
Simplifying further:
Arc Length = (13/36) * (2 * π * 3.6 inches)
Arc Length ≈ 0.361049 * 22.619467 inches
Arc Length ≈ 8.156143 inches
Rounding to the nearest thousandth, the arc length is approximately 8.156 inches.