Cylindrical Shell ಅನ್ನು ಹೇಗೆ ಲೆಕ್ಕ ಹಾಕುವುದು
Cylindrical Shell ಎಂದರೇನು?
Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
ಸೂತ್ರ
Volume = 2π ∫ x × f(x) dx (shell method)
ಹಂತ-ಹಂತದ ಮಾರ್ಗದರ್ಶಿ
- 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
Worked Examples
ಇನ್ಪುಟ್
R=5, r=3, h=10
ಫಲಿತಾಂಶ
V 502.7
Common Mistakes to Avoid
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
Frequently Asked Questions
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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