Ako vypočítať Cylindrical Shell
Čo je Cylindrical Shell?
Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Vzorec
Volume = 2π ∫ x × f(x) dx (shell method)
Sprievodca krok za krokom
- 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
Vstup
R=5, r=3, h=10
Výsledok
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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