Find the arc length of a circle that has a central angle of 270 degrees and a radius of 10 yards.
To find the arc length of a circle, you can use the formula:
Arc Length = (θ/360) * 2 * π * r
where:
- θ is the central angle in degrees
- r is the radius of the circle
- π is a mathematical constant approximately equal to 3.14159
In this case, the central angle is 270 degrees and the radius is 10 yards. So, we can plug in these values into the formula to find the arc length:
Arc Length = (270/360) * 2 * π * 10
Simplifying:
Arc Length = (3/4) * 2 * π * 10
Arc Length = (3/2) * π * 10
Arc Length = 15 * π
Therefore, the arc length of a circle with a central angle of 270 degrees and a radius of 10 yards is 15π yards.
s = rθ
just plug in your numbers (in radians)