Area of an Annulus Calculator
Created By : Abhinandan Kumar
Reviewed By : Rajashekhar Valipishetty
Last Updated : Apr 24, 2023
Area of an Annulus (Ring) Calculator: Understanding the step by step procedure of computing the area of an annulus helps the students to solve the math questions easily in their assignments and exams. Area of an Annulus Calculator is a free and handy tool that gives the exact solution within seconds. This calculator aims to save the valuable time of the students while solving the tough math problems. You need to enter the outer radius, inner radius of an annulus circle in the input fields and also select the units, hit on the calculate button to find the area in a short span of time.
Annulus Ring Area Formula
The formula for area of an annulus is given below
Area of an annular ring is A = π * (R² - r²)
Where, R is the radius of an outer circle.
r is the radius of an inner circle.
If you know diameter of annulus circle,
Area of an annulus (ring) is A = (π / 4) * (D² - d²)
d is the diameter of inner circle.
D is the diameter of outer circle.
Steps to Calculate the Area of an Annular Ring
Have a look at the manual procedure to calculate the annulus ring area in the below sections. Follow these simple steps and guidelines to get the area of an annulus using the formula.
- Get the inner circle radius and outer circle radius from the question.
- Square the radius of both circles.
- Find the difference of outer circle square and inner circle radius.
- Multiply the obtained value with π.
- The result is called area of an annulus (ring).
Examples of Annulus Ring Area
Example 1: Find the area of the path, where the path is 16 cm wide, surrounds a circular lawn whose diameter is 360 cm?
Width of the path = 16 cm
Diameter of inner circle = 360 cm
Radius of inner circle (r) = diameter / 2 = 360 / 2 = 180
Radius of the outer circle (R) = 180 + 16 = 196
Area of annulus = π * (R² - r²)
A = 3.14 * (196² - 180²)
= 3.14 * (38416 - 32400)
= 3.14 * 6016
∴ Area of an annulus is 18890.24 cm².
Example 2: If the area of an annulus is equal to 1092 inches and its width is equal to 2 inches, then find the radius of both inner and outer circles?
Area of annulus = 1092 inches
Width of annulus = 2 inches
Width is equal to R - r
R - r = 2
R = 2 + r
The formula to calculate area of an annulus A = π * (R² - r²)
= π * (R - r) * (R + r)
Substitute the values in the above formula.
1092 = π * (2 + r - r) * (2 + r + r)
1092 = 2π * (2r + 2)
1092 = 4π * (r + 1)
= 3.14 * 4 * (r + 1)
= 12.56 * (r + 1)
1092 / 12.56 = r + 1
86.94 = r + 1
r = 86.94 - 1
r = 85.94
R - r = 2 inches
R - 85.94 = 2
R = 2 + 85.94
So, the radius of outer circle is 87.94 inches, radius of inner circle is 85.94 inches.
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FAQ's on Annulus Area
1. What is meant by annulus?
Annulus is an region basically defined as the shape out of two circles. It is formed by two concentric circles. The region covered between those concentric circles is called annulus or annular region.
2. What is the area of an annulus ring?
Area of an annulus (ring) is defined as the area that is covered between the concentric circles. It can be obtained by finding the area of an inner circle meaning smaller one and area of an outer circle meaning bigger one. Subtract those two values to get the final result.
3. What are the examples of Annulus ring?
Some of the annulus ring examples are dough-nut, finger-ring, and others.
4. What are the formulas to find the inner circle, outer circle radii?
Radius of outer circle R = √(r² + (A) /( π))
Radius of inner circle r = √(R² - (A) /( π))
Where, A is the area of annulus and π is 22 / 7.