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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Wzór
Volume = 2π ∫ x × f(x) dx (shell method)
Przewodnik krok po kroku
- 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
Rozwiązane przykłady
Wejście
R=5, r=3, h=10
Wynik
V 502.7
Częste błędy do unikania
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Często zadawane pytania
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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