The-surface-area-of-a-cylinder-is-A-2pir-2-2pirh-As-h-0-the-shape-becomes-a-2D-circle-so-should-lim-h-0-A-pir-2-Or-is-it-that-as-h-0-it-creates-a-circle-of-3-dimensions-with-infinte

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Question Number 5542 by FilupSmith last updated on 19/May/16

$$\mathrm{The}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{cylinder}\mathrm{is}:$$$$A=2\pi r^2+2\pi rh$$$$$$$$\mathrm{As}h\to 0,\mathrm{the}\mathrm{shape}\mathrm{becomes}\mathrm{a}2\mathrm{D}\mathrm{circle},$$$$\mathrm{so}\mathrm{should}\underset{h\to 0}{\lim }A=\pi r^2???$$$$\mathrm{Or}\mathrm{is}\mathrm{it}\mathrm{that}\mathrm{as}h\to 0,\mathrm{it}\mathrm{creates}\mathrm{a}\mathrm{circle}$$$$\mathrm{of}3\mathrm{dimensions}\mathrm{with}\mathrm{infintesimally}\mathrm{small}$$$$\mathrm{height},\mathrm{so}\mathrm{it}\mathrm{has}\mathrm{two}\mathrm{circles}\mathrm{making}\mathrm{it}:$$$$\underset{h\to 0}{\lim }A=2\pi r^2???$$

Commented by FilupSmith last updated on 19/May/16

$$\mathrm{That}\mathrm{is}\mathrm{also}\mathrm{what}\mathrm{i}\mathrm{thought}!$$

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