A tube (hollow cylinder) has an outer radius R and inner radius r. Volume = π(R² − r²) × length. Surface area includes outer surface, inner surface, and the two ring-shaped ends. Used for pipes, ducts, and hollow shafts.
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Pro Tip
For fluid flow, the flow area is π r_inner². Pipe capacity scales as the square of the internal radius — doubling the pipe diameter quadruples the flow capacity (for the same pressure).
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Did You Know?
Hollow tubes are remarkably efficient structural members. A hollow steel tube (pipe) has nearly the same bending strength as a solid bar of the same weight but with much less material. This is why bicycle frames and aircraft use tubing — maximum strength per unit weight.
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