Cylinder Calculator
V = πr²h | SA = 2πr(r + h)
r =
h =
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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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).
- 1Wall thickness = R − r (outer minus inner radius)
- 2Cross-sectional area = π(R² − r²)
- 3Volume = π(R² − r²) × length
- 4Total SA = 2π(R+r)×length + 2π(R²−r²) (lateral + ends)
Outer R=5, inner r=3, length=20=V = π(25−9)×20 = 1,005.3 cubic unitsWall thickness = 2 units
| Property | Solid cylinder | Tube (R=5, r=3, h=20) |
|---|---|---|
| Volume | πr²h = 1,570.8 | 1,005.3 (64% of solid) |
| Material | 100% | 64% of solid |
| Strength/weight | Lower | Higher |
| Common use | Shafts, bars | Pipes, structural tubing |
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Fun Fact
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.
References
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