Kuinka laskea Cylindrical Shell
Mikä on Cylindrical Shell?
Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
Kaava
Volume = 2π ∫ x × f(x) dx (shell method)
Vaiheittainen opas
- 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
Ratkaistut esimerkit
Syöte
R=5, r=3, h=10
Tulos
V 502.7
Yleisiä virheitä vältettäväksi
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Usein kysytyt kysymykset
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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