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In my physics lab, I am asked to calculate the volume of a hollow cylinder. The equation for the volume hollow cylinder below was given. Then, my curiosity made me wonder, is the volume of the hollow cylinder the same as the volume of a cylindrical shell used in calculus? At first though you would assume the answer as yes. However, I have tested this theory using various measurements, resulting in two different results. Can anyone help me understand why Hallow Cylinder does not equal Cylindrical Shell? or maybe disprove my results.
Hollow Cylinder =
(π)(height)((r_{o})2−(r_{i})2)
Cylindrical Shell = 2(π)(r_{i})(height)(thickness)
The subscript "o" means outer-radius, and "i" means inter-radius
Hollow Cylinder =
(π)(height)((r_{o})2−(r_{i})2)
Cylindrical Shell = 2(π)(r_{i})(height)(thickness)
The subscript "o" means outer-radius, and "i" means inter-radius