So berechnen Sie Cylindrical Shell
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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Formel
Volume = 2π ∫ x × f(x) dx (shell method)
Schritt-für-Schritt-Anleitung
- 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
Gelöste Beispiele
Eingabe
R=5, r=3, h=10
Ergebnis
V 502.7
Häufige Fehler vermeiden
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Häufig gestellte Fragen
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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