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Annulus Formulas in terms of radius r: (Π = Pi)

• Calculate the outer circumference of an annulus:
  • c1 = 2 * Π * r1
• Calculate the inner circumference of an annulus:
• c2 = 2 * Π * r2
• Calculate the surface area of the space enclosed by the outer circle
• a1 = Π * r1^2
• Calculate the surface area of the space enclosed by the inner circle
• a2 = Π * r2^2
• Calculate the surface area of the annulus (the grey shaded area)
• a0 = a1 - a2

Annulus Calculations:

Use the following additional formulas along with the formulas above.

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 calculate the outer circumference, the inner circumference and the area of the shaded section of the annulus.
  Given r1 and r2 find c1, c2 and a0
  • 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 calculate the outer radius, the inner radius and the area of the shaded section of the annulus.
  Given c1 and c2 find r1, r2 and a0
  • 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 calculate the outer circumference, the inner radius and the area of the shaded section of the annulus.
  Given r1 and c2 find r2, c1 and a0
  • 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 calculate the outer radius, inner circumference and the area af the shaded section of the annulus.
  Given r2 and c1 find r1, c2 and a0
  • 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 calculate the inner radius, the outer circumference and the inner circumference of the annulus.
  Given a0 and r1 find c1, c2 and r2
  • 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 calculate the outer radius, the outer circumference and the inner circumference of the annulus.
  Given a0 and r2 find c1, c2 and r1
  • 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 calculate the inner circumference, the outer radius and the inner radius of the annulus.
  Given a0 and c1 find r1, r2 and c2
  • 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 calculate the outer circumference, the outer radius and the inner radius of the annulus.
  Given a0 and c2 find r1, r2 and c1
  • r2 = c2 / (2 * Π)
  • a2 = Π * r2^2
  • a1 = a0 + a2
  • r1 = square root (a1 / Π )
  • c1 = 2 * Π * r1