What is Arc Length?
You must have heard about circles and arcs. The circle is one of the basic shapes taught in earlier standards. It is also an interesting shape to learn, arcs, radius, diameter is important part of the circle. An arc is a part of the circumference of a circle or a part of a curve. Arc length is the distance between two points along the curved line or along the circumference of a circle. In other words, the distance from one point to another point along the curve is called the arc length. It is to be noted that the length through the curved line of the circle circumference joining two endpoints on the curve is always more than the length of the straight line joining the same two points.
The angle produced by the two lines joining the center to the two endpoints of the arc is called the central angle. To calculation the length of arc, different methods are applied. The calculations are done according to the unit of the central angle of the arc. The unit of the central angle can be measured in degrees or radians, and accordingly, the arc length of a circle is calculated. We will earn about these with an example. One of the interesting concepts of a circle is that the diameter of the circle is the longest chord, and the perimeter of the circle is called the circumference of the circle which is equal to 2 π r. As an arc is a part of the circumference of the circle, the arc length formula uses the given formula. So let’s learn more about it.
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In a circle, the arc length is calculated using the given data with the help of different formulas. There are some important methods of calculation for arc length that is given below:
- Finding arc length using the measurement of radius and central angle
- Finding arc length using the measurement of radius
- Finding arc length without the measurement of the central angle
Examples of Arc Length Formula Using Degrees
Let’s learn how to find the length of an arc if radius and central angle are given. Check out the example below:
If the radius of the arc is 8 cm and the angle is 40 degrees then,
Arc length can be found using the formula: s = 2 π r (θ/360°)
S = 2 * 3.14 * 8 * (40 /360) = 5.582 cm
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