Find the length of the arc on a circle of radius
7 ft intercepted by a central angle 220◦
.
Answer in units of ft
220/360 of the full circumference
To find the length of the arc on a circle, you can use the formula:
Arc Length = (Central Angle / 360°) * 2πr
Where:
- Arc Length is the length of the arc
- Central Angle is the measure of the angle intercepted by the arc
- r is the radius of the circle
- π is a mathematical constant, approximately equal to 3.14159
In this case, the radius is given as 7 ft and the central angle is given as 220°. Plugging these values into the formula, we have:
Arc Length = (220° / 360°) * 2π * 7 ft
To calculate this, we need to convert the angle from degrees to radians. Since 1 radian is equal to 180°/π, we can convert 220° to radians as:
220° / 180° * π ≈ 3.83 radians
Now, substituting this value into the formula, we get:
Arc Length = (3.83 radians / 360°) * 2π * 7 ft
Simplifying further:
Arc Length ≈ (0.0106 radians) * (2π * 7 ft)
Arc Length ≈ 0.0727π ft
Finally, using the value of π as approximately 3.14159:
Arc Length ≈ 0.0727 * 3.14159 ft
Arc Length ≈ 0.2283 ft
Therefore, the length of the arc on a circle with a radius of 7 ft and intercepted by a central angle of 220° is approximately 0.2283 ft.