Annulus
An annulus is an inner region between two concentric circles i.e. two or more circles sharing the same center point. The annulus is shaped like a ring and has many applications in mathematics that we will be learning in this article. Some of the real-life examples are a doughnut, finger rings. etc. Let us learn more about the shape of the annulus and solve a few examples to understand the concept better.
| 1. | Definition of Annulus |
| 2. | Area of Annulus |
| 3. | Perimeter of Annulus |
| 4. | FAQs on Annulus |
Annulus Definition
An annulus is a two-dimensional flat figure shaped in a circular form which is constructed by two concentric circles. The region or the area formed in between these two concentric circles is called the annulus. Since it is a flat figure in a circular form, the edges are two circles with the same center. It is considered a circular disk having a circular hole in the middle.
Annulus Meaning
The word annulus is derived from a Latin word, 'annuli', meaning little rings. The shape of the annulus is flat and circular with a hole in between, much like a throw ring or a circular disc. Look at the image below showing two circles i.e. one small circle also called an inner circle and a big circle also called the outer circle. The point which is marked as red is the center of both circles. The shaded colored area, between the boundary of these two circles, is known as an annulus.
Area of the Annulus
The annulus area is the area of the ring-shaped space i.e. the enclosed region between the two concentric circles. To calculate the area of the annulus, we need the area of both the inner circle and the outer circle. The dimensions of an annulus are defined by the two radii R, and r, which are the radii of the outer ring and the inner ring respectively. Once the measurements of both the radii are known, we can calculate the area by subtracting the area of the small circle from the big circle. Hence, the formula used for finding the area of the annulus is:
Area of Outer Circle = πR2
Area of Inner Circle = πr2
Area of Annulus = Area of Outer Circle – Area of Inner Circle
Therefore, Area of Annulus = π(R2-r2) square units, or it can be written as π(R+r)(R-r) square units, where R is the radius of the outer circle, r is the radius of the inner circle, and π(pi) is approximately 3.142. Look at the image below, the area of the outer (bigger) circle - the area of the inner (smaller) circle = the area of the annulus.
Annulus Perimeter
The perimeter is the distance around the 2D shape. Since the annulus is a flat circular shape constructed by two concentric circles, it can also be considered as a ring. Therefore, an open ring can be considered as the topological equivalent of a cylinder and a punctured plane. Similar to the area, to find the perimeter of the annulus we need to consider both the inner circle and the outer circle. So, the perimeter of the ring or annulus is equal to the sum of the radii of the large and small circles multiplied by 2π. The formula for finding the perimeter is:
Perimeter of Annulus (P) = 2π(R+r) units, where R is the radius of the outer circle, r is the radius of the inner circle, and π (pi) is approximately 3.142.
Related Topics
Listed below are a few relatable topics to the annulus, take a look!
FAQs on Annulus
What is the Meaning of the Word Annulus?
The word annulus is derived from the Latin word annuli which means little rings. It is a 2D flat figure which is circular in nature but a hole in between like a doughnut. An annulus is the region enclosed between the boundary of these two circles.
What is Annulus Area?
The annulus area is the area of the ring-shaped i.e. the region enclosed between the two concentric circles. To calculate the area of the annulus, the areas of both the inner circle and the outer circle are required.
Area of Outer Circle = πR2
Area of Inner Circle = πr2
Based on these, the formula for the area of the annulus is area of outer circle – area of inner circle. Therefore, Area of Annulus = π(R2-r2) square units, where R is the radius of the outer circle, r is the radius of the inner circle, and π (pi) is approximately 3.142.
What is the Perimeter of the Annulus?
Annulus perimeter is considered as the entire distance around the 2D shape including both the inner circle and the outer circle. The formula to find the perimeter of the annulus is 2π(R+r) units, where R is the radius of the outer circle, r is the radius of the inner circle, and π (pi) is approximately 3.142.
Is a Circle an Annulus?
In mathematics, an annulus is a region between two concentric circles. It is shaped like a ring or a donut. A circle is not an annulus since it is a completely closed figure in a circular manner, whereas an annulus is a circular-shaped figure but with a hole in between.
What is Annulus Radius?
The annulus radius is the difference between the radius of the outer circle and the inner circle. Since an annulus is constructed by two concentric circles, the radius of both the circles is required. The dimensions of the annulus radius are derived from the radii of the outer circle and inner circle with R and r as the measures respectively.
What Dimension is an Annulus?
An annulus is a two-dimensional shape that is flat and circular in nature. It is constructed by two concentric circles with a hole in between and that enclosed region is called the annulus.