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Notes:
Area of the annulus between r1 and r2, the shaded area, is the area contained by the outer circle minus the area contained by the inner circle or a0 = a1 - a2.
You will need to know 2 items of information in order to calculate the remainder of variables. The following are the formulas we used in our calculations:
Given outer radius and inner radius of the annulus find the outer circumference, the inner circumference and the area of the shaded section of the annulus.
- c1 = 2 * Π * r1
- c2 = 2 * Π * r2
- a1 = Π * r1^2
- a2 = Π * r2^2
- a0 = a1 - a2
Given outer circumference and inner circumference of the annulus you can find the outer radius, the inner radius and the area of the shaded section of the annulus.
- r1 = c1 / (2 * Π )
- r2 = c2 / (2 * Π )
- a1 = Π * r1^2
- a2 = Π * r2^2
- a0 = a1 - a2
Given outer radius and inner circumference of the annulus find the outer circumference, the inner radius and the area of the shaded section of the annulus.
- c1 = 2 * Π * r1
- r2 = c2 / (2 * Π)
- a1 = Π * r1^2
- a2 = Π * r2^2
- a0 = a1 - a2
Given inner radius and outer circumference find the outer radius, inner circumference and the area af the shaded section of the annulus.
- c2 = 2 * Π * r2
- r1 = c1 / (2 * Π)
- a1 = Π * r1^2
- a2 = Π * r2^2
- a0 = a1 - a2
Given area of the shaded section and the outer radius find the inner radius, the outer circumference and the inner circumference of the annulus.
- c1 = 2 * Π * r1
- a1 = Π * r1^2
- a2 = a1 - a0
- r2 = square root (a2 / Π)
- c2 = 2 * Π * r2
Given area of the shaded section and the inner radius find the outer radius, the outer circumference and the inner circumference of the annulus.
- c2 = 2 * Π * r2
- a2 = Π * r2^2
- a1 = a0 + a2
- r1 = square root (a1 / Π)
- c1 = 2 * Π * r1
Given area of the shaded section and the outer circumference find the inner circumference, the outer radius and the inner radius of the annulus.
- r1 = c1 / (2 * Π)
- a1 = Π * r1^2
- a2 = a1 - a0
- r2 = square root (a2 / Π )
- c2 = 2 * Π* r2
Given area of the shaded section and the inner circumference find the outer circumference, the outer radius and the inner radius of the annulus.
- r2 = c2 / (2 * Π)
- a2 = Π * r2^2
- a1 = a0 + a2
- r1 = square root (a1 / Π )
- c1 = 2 * Π * r1
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r1 = outer radius
r2 = inner radius
a0 = shaded area
c1 = outer circumference
c2 = inner circumference
Π = Pi
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