Hollow Cylinder Volume Calculator
Calculate volume, thickness, and properties of hollow cylindrical shells
Calculate Hollow Cylinder Volume
Height of the cylinder
Outer diameter of cylinder
Inner diameter of hollow space
Hollow Cylinder Properties
Formulas Used:
Basic Formula: VH = Vouter - Vinner
Volume: VH = π(R² - r²)h
With Diameters: VH = π(D² - d²)h/4
With Thickness: VH = π(t² + 2tr)h
Cross-Section: A = π(R² - r²)
Thickness: t = R - r
Example Calculation
Example: Pipe Volume
Problem: Calculate volume of a pipe with outer diameter D = 8 cm, inner diameter d = 4 cm, and height h = 12 cm
Given: D = 8 cm, d = 4 cm, h = 12 cm
Solution
Step 1: Calculate radii - R = D/2 = 8/2 = 4 cm, r = d/2 = 4/2 = 2 cm
Step 2: Cross-sectional area = π(R² - r²) = π(4² - 2²) = π(16 - 4) = 37.7 cm²
Step 3: Volume = Cross-sectional area × height = 37.7 × 12 = 452.4 cm³
Alternative: VH = π(D² - d²)h/4 = π(64 - 16) × 12/4 = 452.4 cm³
Hollow Cylinder Components
Outer Cylinder
Larger cylinder with radius R
Volume = πR²h
Inner Cylinder
Smaller cylinder with radius r
Volume = πr²h
Shell Volume
Material between cylinders
Volume = π(R² - r²)h
Thickness
Wall thickness t = R - r
Alternative formula available
Calculation Tips
Can use diameters, radii, or thickness for input
Volume equals outer cylinder minus inner cylinder
Common in pipes, tubes, and containers
Cross-sectional area helps with material calculations
Understanding Hollow Cylinders
What is a Hollow Cylinder?
A hollow cylinder is a three-dimensional shape formed by subtracting one cylinder from another larger cylinder that shares the same central axis. This creates a cylindrical shell with a hollow interior space.
Real-World Applications
- •Pipes and tubes for plumbing and construction
- •Bottles, jars, and containers
- •Structural steel columns and beams
- •Engine cylinders and pistons
- •Chemical reactors and pressure vessels
Volume Calculation Methods
Basic Subtraction: VH = Vouter - Vinner
Direct Formula: VH = π(R² - r²)h
Using Diameters: VH = π(D² - d²)h/4
With Thickness: VH = π(t² + 2tr)h
Key Relationships
- • Thickness: t = R - r
- • Outer diameter: D = 2R
- • Inner diameter: d = 2r
- • Cross-sectional area: A = π(R² - r²)
- • Material volume equals shell volume
Note: Hollow cylinders are also called cylindrical shells or annular cylinders