如何计算Cylindrical Shell
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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
公式
Volume = 2π ∫ x × f(x) dx (shell method)
分步指南
- 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
例题解析
输入
R=5, r=3, h=10
结果
V 502.7
常见错误注意事项
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
常见问题
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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