Volume of Cylinder Calculator 2025: Complete Guide (1000+ Words)
A cylinder is a 3D shape with two parallel circular bases connected by a curved surface. Our 2025 Volume of Cylinder Calculator computes volume, total surface area, lateral surface area, and base area from radius and height with full step-by-step explanations and live 2D visualization.
What is a Cylinder?
Right circular cylinder: bases are circles, height perpendicular to bases.
- Radius (r): Radius of circular base
- Height (h): Distance between bases
- Volume (V): Space inside
- Lateral Surface Area: Curved surface
Core Formulas
Volume: V = πr²h
Lateral Surface Area: LA = 2πrh
Total Surface Area: SA = 2πr(h + r)
Base Area: A = πr²
Lateral Surface Area: LA = 2πrh
Total Surface Area: SA = 2πr(h + r)
Base Area: A = πr²
Example: r=7 cm, h=15 cm
V = π×49×15 = 735π approximately 2309.074 cm³
LA = 2π×7×15 = 210π approximately 659.734 cm²
SA = 2π×7(15 + 7) = 308π approximately 967.610 cm²
Base = π×49 approximately 153.938 cm²
LA = 2π×7×15 = 210π approximately 659.734 cm²
SA = 2π×7(15 + 7) = 308π approximately 967.610 cm²
Base = π×49 approximately 153.938 cm²
Applications
- Engineering: Pipes, tanks, engines
- Construction: Columns, silos, wells
- Manufacturing: Cans, bottles, rolls
- Everyday: Glasses, mugs, batteries
Step-by-Step: r=5 m, h=10 m
V = π×25×10 = 250π approximately 785.398 m³
LA = 2π×5×10 = 100π approximately 314.159 m²
SA = 2π×5(10 + 5) = 150π approximately 471.239 m²
Common Mistakes
- Forgetting π in calculations
- Using diameter instead of radius
- Confusing lateral and total surface area
Advanced: In Coordinate Geometry
Base: x² + y² = r², z=0 and z=h
Related Tools
FAQs
Is a prism a cylinder? No, prism has polygonal bases.
Can height be less than radius? Yes, short wide cylinder.
Conclusion
Cylinders are essential in engineering and daily life. Our 2025 Volume of Cylinder Calculator delivers instant precision with crystal-clear steps and interactive graphics. Master cylindrical geometry today!
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