How to Calculate Cylindrical Shell
What is Cylindrical Shell?
Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Formula
Volume = 2π ∫ x × f(x) dx (shell method)
Step-by-Step Guide
- 1Volume = 2π ∫ x × f(x) dx (shell method)
- 2Or Volume = π(R² - r²) × h where R = outer, r = inner, h = height
- 3Surface area = 2πRh + 2πrh + 2π(R² - r²)
- 4Thickness = R - r
Worked Examples
Input
R=5, r=3, h=10
Result
V 502.7
Common Mistakes to Avoid
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Frequently Asked Questions
What practical examples are cylindrical shells?
Pipes, tubing, hollow cylinders, insulation layers on pipes.
Why use shell method vs. disk method?
Shell method easier when axis is axis of symmetry; disk method when perpendicular.
Ready to calculate? Try the free Cylindrical Shell Calculator
Try it yourself →