Arc length – A crucial concept of circles

We come across various shapes and figures in our everyday life. All the shapes have one or more properties that are not only different from all other shapes but also make them unique. In this article, we will be focusing on one of the crucial concepts of circles. The arc length formula of a circle is the concept that we will be discussing in this article. It is a critical topic, and its understanding is a must for every student because it has a lot of real-life applications. 

Circle: This is one of the fundamental forms that we all learn about. A two-dimensional shape is a circle. A circle is one of the few forms that does not have any edges or corners. It has no sides or corners and is fully circular. There are a number of important ideas to understand when it comes to circles, but the radius and diameter are the most important to learn before moving on to other features.

When constructing a circle, there is one requirement that must be known: the radius or diameter of the circle. The longest chord inside a circle is the diameter of the circle, which always crosses the circle’s midway. A diameter’s endpoints are always perfectly opposite each other. Another thing to remember about the diameter’s endpoints is that they are always on the circle. A radius is simply defined as half of a circle’s diameter.

Arc length of a circle: Arc length is nothing else but the distance between two points along the section of the curve of the circle. When we join any two points on the curve of the circle it forms an angle as well. To calculate the arc length of a circle, one can use the arc length formula. It is one of the easiest and accurate methods of calculating arc length.

The arc length formula is simple, and not many elements are involved in it. One just needs to have the value of the radius of the circle and the angle subtended by that arc. To calculate arc length, we just have to multiply the angle subtended by the arc and the radius of the circle. Thus, the arc length formula looks like L = theta x radius. In the above-written formula, L is the arc length that we have to find, theta is the angle subtended by the arc. One point to keep in mind while applying this formula is that the angle should be in radians. 

Angles play a huge role in arc length formulas. One should always keep in mind while solving problems related to arc length whether the angle given is in radians or degree. If the angle is given in angle, then one has to do a bit of modification in the formula before using it to calculate the arc length. Let us look at the formula to use if the angle is given in degrees. Let L be the arc length, then it is given by the radius multiplied by the angle subtended by the arc and finally multiplying it with π/180. One can represent it as L = radius x theta x π/180, where L is the arc length. 

In the above article, we have discussed circles and arc length formulas. It is essential for every student to master these topics as they have huge importance and are commonly used in various subjects. If students face any kind of difficulty in understanding such math-related topics, they should visit website of Cuemath. It is a platform that provides quality education to all students. Students facing any kind of problem in maths should visit this website.