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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Formel
Volume = 2π ∫ x × f(x) dx (shell method)
Trinn-for-trinn guide
- 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
Løste eksempler
Inndata
R=5, r=3, h=10
Resultat
V 502.7
Vanlige feil å unngå
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Ofte stilte spørsmål
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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