Annulus Area
An annulus is the region between two concentric circles, so its area is found by subtracting the area of the smaller circle from the area of the larger circle.
Method
- Identify the two radii: the outer radius and the inner radius.
- Find each circle’s area using (A = \pi r^2).
- Subtract:
[
A_{\text{annulus}} = \pi R^2 - \pi r^2 = \pi(R^2 - r^2)
]
where (R) is the outer radius and (r) is the inner radius.
- Simplify the result as much as possible.
Good habits
- Make sure both radii use the same units.
- Square the radii before subtracting; do not subtract the radii first.
- Keep (\pi) in exact form unless the problem asks for a decimal.
Check your work
- The answer should be an area, so it must be in square units.
- Since the outer circle is larger, the final area should be positive.
- If you estimate, the annulus area should be smaller than the area of the outer circle and larger than 0.
This method works every time: find the two circle areas, subtract, and simplify.