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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Fórmula
Volume = 2π ∫ x × f(x) dx (shell method)
Guia passo a 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
Exemplos resolvidos
Entrada
R=5, r=3, h=10
Resultado
V 502.7
Erros comuns a evitar
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Perguntas frequentes
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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