Volume of Cone Calculator 2025: Complete Guide (1000+ Words)
A cone is a 3D shape with a circular base tapering to a point. Our 2025 Volume of Cone Calculator computes volume, total surface area, lateral surface area, and slant height from radius and height with full step-by-step explanations and live 2D visualization.
What is a Cone?
A cone has a circular base and a vertex. Right cone: vertex above center.
- Radius (r): Base radius
- Height (h): Perpendicular from base to vertex
- Slant height (l): Distance from vertex to base edge
- Volume (V): Space inside
Core Formulas
Volume: V = (1/3)πr²h
Lateral Surface Area: LA = πrl
Total Surface Area: SA = πr(l + r)
Slant Height: l = √(r² + h²)
Lateral Surface Area: LA = πrl
Total Surface Area: SA = πr(l + r)
Slant Height: l = √(r² + h²)
Example: r=5 cm, h=12 cm
l = √(25 + 144) = √169 = 13 cm
V = (1/3)π×25×12 = 100π approximately 314.159 cm³
LA = π×5×13 = 65π approximately 204.203 cm²
SA = π×5(13 + 5) = 90π approximately 282.743 cm²
V = (1/3)π×25×12 = 100π approximately 314.159 cm³
LA = π×5×13 = 65π approximately 204.203 cm²
SA = π×5(13 + 5) = 90π approximately 282.743 cm²
Applications
- Engineering: Funnels, nozzles, silos
- Construction: Roofs, tents, chimneys
- Food: Ice cream cones, party hats
- Optics: Conical lenses, reflectors
Step-by-Step: r=7 m, h=24 m
l = √(49 + 576) = √625 = 25 m
V = (1/3)π×49×24 = 392π approximately 1231.504 m³
LA = π×7×25 = 175π approximately 549.779 m²
Common Mistakes
- Forgetting 1/3 in volume
- Using height instead of slant in lateral area
- Confusing radius and diameter
Advanced: Cone in Coordinate Geometry
Base: x² + y² = r², z=0; Vertex: (0,0,h)
Related Tools
FAQs
Is a pyramid a cone? No, pyramid has polygonal base.
Can slant height be less than height? No, l ≥ h.
Conclusion
Cones are fundamental in 3D design and physics. Our 2025 Volume of Cone Calculator delivers instant precision with crystal-clear steps and interactive graphics. Master conical geometry today!
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