Volume of Cylinder Calculator
Volume of a cylinder from radius and height.
Formula first
Overview
The volume of a cylinder represents the total three-dimensional space occupied by a solid with two parallel circular bases. It is calculated by taking the area of the base (πr²) and extending it through the perpendicular height (h) of the object.
Symbols
Variables
r = Radius, h = Height, V = Volume
Apply it well
When To Use
When to use: Use this formula when calculating the capacity of containers with a uniform circular cross-section, such as pipes, tanks, or jars. It assumes the cylinder is a 'right cylinder', meaning the height is perfectly perpendicular to the base.
Why it matters: This equation is vital in fluid dynamics and mechanical engineering for determining the displacement of pistons or the volume of fuel stored in silos. It helps professionals calculate material costs for manufacturing cylindrical components and estimate the weight of liquid contents.
Avoid these traps
Common Mistakes
- Using diameter instead of radius (diameter = 2r)
- Forgetting to square the radius
- Forgetting π in the calculation
- Mixing units (e.g., radius in cm but height in m)
One free problem
Practice Problem
Find the volume of a cylindrical silo with a radius of 4 m and a height of 10 m.
Solve for:
Hint: V = π * r² * h.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Cylinder
- Britannica: Cylinder (mathematics)
- Halliday, Resnick, Walker, Fundamentals of Physics
- Halliday, Resnick, Walker, *Fundamentals of Physics*, 11th ed.
- NIST Guide for the Use of the International System of Units (SI), Special Publication 811
- Wikipedia: Volume of a cylinder
- Wikipedia: Cylinder (geometry)
- Britannica: Cylinder