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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Formula
Volume = 2π ∫ x × f(x) dx (shell method)
Guida passo passo
- 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
Esempi risolti
Ingresso
R=5, r=3, h=10
Risultato
V 502.7
Errori comuni da evitare
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Domande frequenti
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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