Cum se calculează Cylindrical Shell
Ce este Cylindrical Shell?
Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Formulă
Volume = 2π ∫ x × f(x) dx (shell method)
Ghid pas cu pas
- 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
Exemple rezolvate
Intrare
R=5, r=3, h=10
Rezultat
V 502.7
Greșeli frecvente de evitat
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Întrebări frecvente
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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