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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
सूत्र
Volume = 2π ∫ x × f(x) dx (shell method)
चरण-दर-चरण मार्गदर्शिका
- 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
हल किए गए उदाहरण
इनपुट
R=5, r=3, h=10
परिणाम
V 502.7
सामान्य गलतियां जिनसे बचना है
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
अक्सर पूछे जाने वाले प्रश्न
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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