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Calculates cylindrical shell volume using disk/washer integration method. Hollow cylinder between two radii.
공식
Volume = 2π ∫ x × f(x) dx (shell method)
단계별 가이드
- 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
풀어진 예시
입력
R=5, r=3, h=10
결과
V 502.7
피해야 할 일반적인 실수
- ✕Using total height instead of incremental; integration is key
- ✕Forgetting both curved and flat surfaces in total surface area
자주 묻는 질문
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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