
An annulus is the region between two concentric circles.^{[1]} The area of the annulus is the difference between the areas of the circles: A = π(r_{1}^{2}  r_{2}^{2}) where r_{1} > r_{2}. Understanding CheckWhat is the area of an annulus with an inner radius of 1m and an outer radius of 3m?Click here for the answer. Answer: The formula for the area of an annulus is A = π(r_{1}^{2}  r_{2}^{2}), r_{1} > r_{2}. Plugging in 3m for r_{1} and 1m for r_{2}, we get A = π(3^{2}1^{2}) = π(91) = π·8 ≈ 25.13.  
Examples of Annulus

1. 
A pipe has an inner radius of 3 cm. It has an outer radius of 3.5 cm.
It is 100 cm long. What is the total volume of the pipe, not including
the empty space inside?
Click here for a hint. 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? Click here for the answer. 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(r_{1}^{2}  r_{2}^{2}), r_{1} > r_{2}. So A = π((3.5 cm)^{2}(3 cm)^{2}) ≈ 3.14159(12.25cm^{2}  9cm^{2}) ≈ 3.14159·3.25 cm^{2} ≈ 10.21 cm^{2}. The volume of the pipe is equal to the area of the base times the height. V ≈ 10.21 cm^{2} · 100 cm V ≈ 1021 cm^{3}. 
2. 
The same pipe is made of a metal alloy with a density of
3g/cm^{3}.
What is the mass of the pipe in challenge 1?
Click here for the answer. Answer: Using dimensional analysis, cm^{3}·g/cm^{3} = gm. So multiplying the two quantities will give the correct result. 1021cm^{3}·3gm/cm^{3} = 3063gm = 3.063kg. 
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