Kā aprēķināt Cylindrical Shell
Kas ir 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)
Soli pa solim ceļvedis
- 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
Ievade
R=5, r=3, h=10
Rezultāts
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.
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