Formula for Area of Overlapping Rings?

In summary, the formula for calculating the area of overlapping rings is A = π * (r<sub>1</sub><sup>2</sup> - r<sub>2</sub><sup>2</sup>), where r<sub>1</sub> and r<sub>2</sub> are the radii of the two overlapping rings. The radii of the overlapping rings can be determined by measuring the distance from the center of each ring to the point where they overlap or by dividing the diameter by 2. This formula can be used for any type of overlapping rings as long as they are circular and the area of overlap is a perfect circle. While there are other methods for calculating the area, this
  • #1
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Could anyone direct me to a formula for the area enclosed by two overlapping rings? Sketch below...

area.jpg


Thanks...
-jg
 
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  • #2
I realize my question was a little bit ambiguous... specifically, the area in terms of the radius of the two circles and the distance between their centers. The rings are identical.

Sorry about that.
-jg
 
  • #3
Also, looking at your attachment appears to require a password.
 
  • #4
OK, should be fixed now. Sorry, once again.
-jg
 

Related to Formula for Area of Overlapping Rings?

1. What is the formula for calculating the area of overlapping rings?

The formula for calculating the area of overlapping rings is A = π * (r12 - r22), where r1 and r2 are the radii of the two overlapping rings.

2. How do I determine the radii of the overlapping rings?

The radii of the overlapping rings can be determined by measuring the distance from the center of each ring to the point where they overlap. Alternatively, if you know the diameters of the rings, you can divide them by 2 to get the radii.

3. Can this formula be used for any type of overlapping rings?

Yes, this formula can be used for any type of overlapping rings, as long as they are circular in shape and the area of overlap is a perfect circle.

4. How accurate is this formula for calculating the area of overlapping rings?

This formula provides an accurate calculation of the area of overlapping rings. However, it may not be precise if the rings are not perfectly circular or if the area of overlap is not a perfect circle.

5. Are there any other methods for calculating the area of overlapping rings?

Yes, there are other methods for calculating the area of overlapping rings, such as using the Pythagorean theorem or breaking the overlapping area into smaller, simpler shapes. However, the formula A = π * (r12 - r22) is the most commonly used and accurate method for calculating the area of overlapping rings.

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