ANNULUS
Definition Of Annulus
Annulus is the area between the two concentric circles having different radii.
More About Annulus
A ring-shaped object is called as 'annulus' in Latin.
Area (A) between two concentric circles with outer radius R and inner radius r is given by, A = Π(R2 - r2).
Examples of Annulus
Two concentric circles with outer radius R and inner radius r are shown in the figure. The region shaded with green color is annulus.
Video Examples: Area of an Annulus
Solved Example Clockple on Annulus
Ques: Find the area enclosed between the two concentric circles of radii 8 cm and 10 cm.
Choices:
A. 38Π square cm
B. 37Π square cm
C. 36Π square cm
D. 40Π square cm
Correct Answer: C
Solution:
Step 1: Required Area = Area of outer circle - Area of inner circle
Step 2: Required Area = Π(10)2 - Π(8)2 [Use circle area formula and substitute.]
Step 3: Required Area = Π(100 - 64) = 36Π square cm [Simplify.]
Quick Summary
- An annulus is a ring-shaped region.
- It is formed by two concentric circles with different radii.
- The area of an annulus is the difference between the areas of the outer and inner circles.
🍎 Teacher Insights
Use visual aids like diagrams to illustrate the concept. Emphasize the difference between the outer and inner radii. Provide practice problems with varying radii values.🎓 Prerequisites
- Area of a circle
- Radius
- Concentric circles
- Pi
Check Your Knowledge
Q1: The outer radius of an annulus is 10 cm and the inner radius is 8 cm. What is the area of the annulus?
Q2: Which formula is used to find the area of an annulus?
Frequently Asked Questions
Q: What does concentric mean?
A: Concentric circles share the same center.
Q: How do I find the area if I only know the radii?
A: Use the formula A = π(R² - r²), where R is the outer radius and r is the inner radius.