PanMaths.comFree Printable Math Formula Reference Sheet
Volume of a Cylinder
Geometry • Grades 6, 7, 8, 9
Geometry
Volume of a Cylinder
Learn how to calculate the 3D volume capacity of a circular cylinder given radius and height.
The Formula
V = πr²h
Used for: Calculating the 3D volume capacity of a circular cylinder given radius and height
VVolume of the cylinder (cubic units)
rRadius of circular base
hPerpendicular height / length
dDiameter of base (2r)
⚡Live Interactive Quick Solver
Instant CalculationCylinder Volume (V):785.40 units³
Exact form: 250π• Step: V = π × 5² × 10 = 785.40
V = \pi r^2 h = \frac{\pi}{4} d^2 h
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🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
🛢️
V = Base Area × HeightCircular base area (πr²) multiplied by vertical height (h).
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Cubic UnitsAnswers are in cm³, m³, in³, or liters (1,000 cm³ = 1 L).
🔄
Cone is ⅓ of CylinderA cone with matching radius and height holds exactly ⅓ the volume.
🎮 Interactive 60-Second Challenge
Test Your Speed: Cylinder Volume Blitz!
Calculate cylinder volume from radius & height (V = πr²h) under time pressure. Includes instant 3D diagrams, step-by-step intermediate checks, and zero ads.
🥫 Cylinder (πr²h)🔮 Sphere (⁴⁄₃πr³)🍦 Cone (⅓πr²h)📦 Prism (l·w·h)
🚀 Play 3D Volume Sprint Free→📝 Worked Examples & Step-by-Step Solutions
Example 1: Given Radius & Height
Problem:
Radius r = 4 cm, height h = 10 cm.1
Formula
V = π × r² × h2
Substitute
V = π × (4)² × 103
Calculate r²
V = π × 16 × 10 = 160π4
Decimal Form
V ≈ 160 × 3.14159 ≈ 502.65 cm³Answer: V = 160π cm³ ≈ 502.65 cm³
💡 Pro Tips & Common Mistakes
Given Diameter
Always divide diameter by 2 before squaring (r = d/2).
Capacity in Liters
Convert cm³ to Liters by dividing by 1,000.
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