Annulus

An annulus is the region between two concentric circles.^[2] The area of the annulus is the difference between the areas of the circles: A = π(r₁² - r₂²) where r₁ > r₂.

Understanding Check

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Answer: The formula for the area of an annulus is A = π(r₁² - r₂²), r₁ > r₂. Plugging in 3m for r₁ and 1m for r₂, we get A = π(3²-1²) = π(9-1) = π·8 ≈ 25.13.

Examples of Annulus

Figure 2: Roll of paper towels

Figure 3: Roll of pipe tape

Figure 4: Pipe. The cross section of a pipe is an annulus.

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Hint: The volume of a cylinder is equal to the area of the base times the height of the cylinder (V = b·h). If the base is an annulus, what is the volume of the pipe?

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Answer: The volume of a pipe is the area of the base of the pipe times the height. The area of the base is A = π(r₁² - r₂²), r₁ > r₂. So A = π((3.5 cm)²-(3 cm)²) ≈ 3.14159(12.25cm² - 9cm²) ≈ 3.14159·3.25 cm² ≈ 10.21 cm². The volume of the pipe is equal to the area of the base times the height. V ≈ 10.21 cm² · 100 cm V ≈ 1021 cm³.

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Answer: Using dimensional analysis, cm³·g/cm³ = gm. So multiplying the two quantities will give the correct result. 1021cm³·3gm/cm³ = 3063gm = 3.063kg.