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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Formule
Volume = 2π ∫ x × f(x) dx (shell method)
Stapsgewijze handleiding
- 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
Uitgewerkte voorbeelden
Invoer
R=5, r=3, h=10
Resultaat
V 502.7
Veelgemaakte fouten om te vermijden
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Veelgestelde vragen
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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