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Volume of a Cone
Geometry • Grades 7, 8, 9, 10
Geometry
Volume of a Cone
Calculate the 3D volume of a circular cone using V = ⅓πr²h.
The Formula
V = 13πr²h
Used for: Finding the 3D volume capacity of a circular cone (exactly 1/3 of a cylinder)
VVolume of the cone (cubic units)
rRadius of circular base
hVertical height
lSlant height: √(r² + h²)
⚡Live Interactive Quick Solver
Instant CalculationCone Volume (V):261.80 units³
Exact: 83.33π• Step: V = (1/3) × π × 5² × 10 = 261.80
V = \frac{1}{3}\pi r^2 h
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🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
🍦
V = ⅓πr²hA cone holds exactly one-third the volume of a cylinder with the same dimensions.
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Slant Height (l) vs Height (h)Use Pythagorean theorem l² = r² + h² to find vertical height.
🎮 Interactive 60-Second Challenge
Test Your Speed: Cone Volume Blitz!
Calculate cone volume from radius & height (V = ⅓πr²h) under time pressure. Includes instant 3D diagrams, step-by-step intermediate checks, and zero ads.
🍦 Cone (⅓πr²h)🥫 Cylinder (πr²h)🔮 Sphere (⁴⁄₃πr³)📦 Prism (l·w·h)
🚀 Play 3D Volume Sprint Free→📝 Worked Examples & Step-by-Step Solutions
Example 1: Radius = 6 cm, Height = 10 cm
Problem:
Find the volume of a cone with radius 6 cm and height 10 cm.1
Formula
V = ⅓ × π × r² × h2
Substitute
V = ⅓ × π × (6)² × 103
Calculate
V = ⅓ × π × 36 × 10 = 120π4
Decimal Form
V ≈ 120 × 3.14159 ≈ 376.99 cm³Answer: V = 120π cm³ ≈ 376.99 cm³
💡 Pro Tips & Common Mistakes
Watch Out for Slant Height
If given slant height l, find vertical height h = √(l² - r²).
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