Cylinder Volume Calculator
Calculate volume of solid and hollow cylinders with radius, diameter, and height
Calculate Cylinder Volume
Calculation Results
Formula Used:
Solid Cylinder Formula: V = π × r² × h
Calculation: V = π × 0² × 0 = 0.00 cm³
Additional Properties
Example Calculations
Soda Can Volume
Problem: Find the volume of a soda can with radius = 3.1 cm, height = 12 cm
Formula: V = π × r² × h
Calculation: V = π × 3.1² × 12 = π × 9.61 × 12 ≈ 362.2 cm³
Result: The can holds about 362 ml (approximately 355 ml for a standard can)
Pipe Volume (Hollow Cylinder)
Problem: Find volume of water in a pipe: outer diameter = 10 cm, inner diameter = 8 cm, length = 100 cm
Formula: V = π × (R² - r²) × h
Calculation: V = π × (5² - 4²) × 100 = π × (25 - 16) × 100 = π × 9 × 100 ≈ 2827 cm³
Result: The pipe contains about 2.83 liters of water
Finding Tank Height
Problem: A cylindrical tank holds 500 liters. If radius = 50 cm, what's the height?
Formula: h = V ÷ (π × r²)
Calculation: h = 500,000 cm³ ÷ (π × 50²) = 500,000 ÷ (π × 2500) ≈ 63.66 cm
Result: The tank height is approximately 64 cm
Cylinder Types
Solid Cylinder
Complete cylinder with no holes
Formula: V = π × r² × h
Hollow Cylinder
Cylinder with inner hole (pipe, tube)
Formula: V = π × (R² - r²) × h
Right vs Oblique
Right: perpendicular sides
Oblique: slanted sides (same formula)
Common Applications
Containers
Cans, bottles, jars, tanks
Pipes & Tubes
Water pipes, gas lines, straws
Construction
Columns, pillars, silos
Engineering
Pistons, hydraulic cylinders
Quick Tips
Radius = Diameter ÷ 2
1 liter = 1000 cm³
π ≈ 3.14159 (built into calculator)
Check units for consistency
Understanding Cylinder Volume
What is a Cylinder?
A cylinder is a three-dimensional geometric shape with two parallel circular bases connected by a curved surface. It's one of the most common shapes in everyday life, found in cans, pipes, tanks, and many other objects.
Volume Formula Breakdown
The cylinder volume formula V = π × r² × h comes from the area of the circular base (π × r²) multiplied by the height. This gives us the total space inside the cylinder.
Hollow Cylinders
For hollow cylinders (like pipes), we subtract the inner cylinder volume from the outer cylinder volume: V = π × (R² - r²) × h, where R is the outer radius and r is the inner radius.
Key Formulas
Solid Cylinder Volume
V = π × r² × h
Where r = radius, h = height
Hollow Cylinder Volume
V = π × (R² - r²) × h
Where R = outer radius, r = inner radius
Reverse Calculations
• Height: h = V ÷ (π × r²)
• Radius: r = √(V ÷ (π × h))
• Diameter: d = 2 × r