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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)
ステップバイステップガイド
- 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
解いた例
入力
R=5, r=3, h=10
結果
V 502.7
避けるべきよくある間違い
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
よくある質問
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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