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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Формула
Volume = 2π ∫ x × f(x) dx (shell method)
Пошаговое руководство
- 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
Решённые примеры
Ввод
R=5, r=3, h=10
Результат
V 502.7
Распространённые ошибки
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Часто задаваемые вопросы
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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