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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Formule
Volume = 2π ∫ x × f(x) dx (shell method)
Guide étape par étape
- 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
Exemples résolus
Entrée
R=5, r=3, h=10
Résultat
V 502.7
Erreurs courantes à éviter
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Questions fréquentes
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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