Cylinder Calculators

Comprehensive collection of calculators for cylinders and cylindrical shapes in 3D geometry

Basic Cylinder Forms

Cylinder (V = πr²h)
Circular cylinder - rotation of rectangle around an axis
Hollow Cylinder Tube
Cylinder with cylindrical cavity - pipes and sleeves
Elliptical Cylinder a ≠ b
Cylinder with elliptical base - two different semi-axes

Modified Cylinder Forms

Oblique Cylinder Inclined
Cylinder with inclined axis - not perpendicular to base
Half Cylinder
Longitudinally halved cylinder - half base area
Truncated Cylinder
Cut cylinder with oblique cutting plane

Cylinder Segments and Sectors

Cylindrical Wedge
Wedge-shaped cylinder section between two radial planes
Cylindrical Sector
Sector-shaped cylinder section with specific central angle
Cylindrical Segment Cap
Cylinder section between chord and cylinder wall

Complex Cylinder Forms

Bicylinder Double
Intersection of two interpenetrating cylinders
Tricylinder Triple
Intersection of three interpenetrating cylinders
Hyperboloid Ruled Surface
Hyperbolic rotation solid - one-sheet hyperboloid

About Cylinders and Cylindrical Solids

Cylinders are fundamental rotation solids with diverse applications in engineering, architecture, and nature:

  • Engineering - Pipes, containers, motors
  • Architecture - Columns, towers, silos
  • Industry - Rollers, cylinders, tanks
  • Nature - Tree trunks, stems
  • Transportation - Wheels, axles, rollers
  • Household - Cans, pots, glasses
Fundamental Cylinder Formulas
Circular Cylinder
Volume: V = πr²h
Surface: M = 2πrh
Hollow Cylinder
V = π(R² - r²)h
Tube volume
Elliptical Cylinder
Volume: V = πabh
Elliptical base
Cylinder Sector
V = (θ/360°)πr²h
Sector portion
Cavalieri's Principle: Bodies with equal cross-sectional areas at every height have the same volume - oblique cylinders also follow the basic formula V = πr²h.

Practical Applications

Mechanical Engineering
  • Engine cylinders: Combustion chambers in engines
  • Hydraulic cylinders: Force transmission with fluids
  • Rollers: Material processing and transport
Construction
  • Columns: Load-bearing structural elements
  • Silos: Storage of bulk materials
  • Towers: Water towers, cooling towers
Process Engineering
  • Reactors: Chemical processes
  • Distillation columns: Material separation
  • Heat exchangers: Tube bundles and shell-and-tube
Daily Life & Design
  • Containers: Cans, bottles, glasses
  • Furniture: Round tables, cylindrical forms
  • Art: Sculptures and design objects
Quick Reference
πr²h
Cylinder Volume
2πrh
Surface Area
2πr²
Base Areas
πabh
Elliptical
π(R² - r²)h
Hollow Cylinder
Historical Context

Archimedes (287-212 BC): Calculated cylinder volume and proved the relationship to the inscribed sphere.

Bonaventura Cavalieri (1598-1647): Developed the principle for volume calculations of oblique bodies.

Modern Application: From steam engines to high-performance reactors in industry.

Properties
🔄 Rotation solid: Rotation of rectangle
📏 Parallel surfaces: Base and top congruent
🏗️ Statics: Good pressure distribution
💧 Flow: Low turbulence
🔧 Manufacturing: Easy production by turning