What Do You Mean by Arc Length?

Generally, we come across the concept of arc length while learning about circles or other curves. In a layman's language, arc length can be described as the distance along with the two points of the circumference of any curve or circles. Suppose you need to cover a distance from point A to point B along the path of a circle. The distance that you will cover from the first point to point B is known as the arc length. The concept of arc length has many real-life applications. Starting from the launching of rockets, to the study of cartography, arc length is used extensively in these areas. Arc length also helps to solve mathematical problems. In this article, we will discuss some important concepts related to arc length along with solving a few examples of the concept.

Calculation of Arc Length without the Radius

The distance that covers the surface of a circle or the circumference of the circle can be defined as the arc length. Steps of finding the arc length of a circle without the radius.

• The first step is to multiply the sector area by 2.

• Then, you may divide the above result by the central angle which is given in radians.

• Thirdly, you shall find the square root of the given result. For instance the square root of √25 = 5.

• The last step is to multiply the resultant value of the square root by the central angle to get the arc length of the circle.

Examples

The mathematical formula to calculate the arc length is Ө * r

where l denotes the arc length, Ө denotes the central angle of the arc and r is the radius of the circle. Some examples related to this topic

Example 1: Find the arc length if the value of sector area is 25 square units and central angle as 2 radians?

Ans: According to the question,

Sector area = 25 square units.

Central angle or Ө = 2 radians.

Now, sector area multiplied by 2 = 25 * 2 = 50.

Then, 50/2 = 25.

The square root of 25 = √25 = 5.

Arc length = 2 * 5 = 10 units.

Therefore, the arc length of the circle is equivalent to 10 units.

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