Q: How do I find annulus area if I know the width and one radius?

If you know the ring width w = R - r and the outer radius R: inner radius r = R - w, then A = pi(R^2 - (R-w)^2) = pi(2Rw - w^2). For R=10 and w=4: A = pi(80 - 16) = 201.06. If you know the inner radius instead: R = r + w, then A = pi((r+w)^2 - r^2) = pi(2rw + w^2).

Question 1

What is the area of an annulus with outer radius 10 and inner radius 6?

Accepted Answer

A = pi x (10^2 - 6^2) = pi x (100 - 36) = pi x 64 = 201.06 square units. This is 64% of the full outer circle area (314.16 sq units). The ring width is 10 - 6 = 4 units.

Question 2

How do I calculate the cross-sectional area of a pipe?

Accepted Answer

A pipe is an annulus. Measure the outer diameter and inner diameter, divide each by 2 to get radii, then apply A = pi(R^2 - r^2). For a pipe with outer diameter 10 cm and wall thickness 1 cm: R = 5, r = 4, A = pi(25-16) = 28.27 cm^2 of material cross-section.

Question 3

What is an annulus in geometry?

Accepted Answer

An annulus (plural: annuli) is the flat, ring-shaped region between two concentric circles. Think of a washer, a donut viewed from above, or a circular running track. The two circles must share the same center point.

Question 4

Can the inner radius be zero?

Accepted Answer

Technically yes, but then the annulus becomes a full circle with area pi x R^2. For the formula to produce a meaningful ring shape, the inner radius must be greater than 0 and less than the outer radius (0 < r < R).

Question 5

How do I find annulus area if I know the width and one radius?

Accepted Answer

If you know the ring width w = R - r and the outer radius R: inner radius r = R - w, then A = pi(R^2 - (R-w)^2) = pi(2Rw - w^2). For R=10 and w=4: A = pi(80 - 16) = 201.06. If you know the inner radius instead: R = r + w, then A = pi((r+w)^2 - r^2) = pi(2rw + w^2).

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