The cylinder's curved looks like a rectangle when unfolded. Since, the cylinder and hemisphere have the same formula for curved surface area - $2\pi r * h$, I assume the hemisphere will also form a rectangle when unfolded similar to how the area of a circle is determined. However, I can not understand how to unfold the hemisphere. A diagram I made to understand the thing.
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3$\begingroup$ A cylinder is flat (curvature 0), so can be unrolled to a piece of paper. A hemisphere is curved, so cannot. $\endgroup$– Ted ShifrinCommented May 10, 2022 at 19:34
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$\begingroup$ Not a duplicate, but probably of interest: math.stackexchange.com/questions/4345667/… $\endgroup$– Andrew D. HwangCommented May 10, 2022 at 20:13
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$\begingroup$ see what happens when you peel off half an orange, and then try to flatten it. it will crack. $\endgroup$– user2661923Commented May 10, 2022 at 20:15
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1 Answer
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A cylinder and a hemisphere do NOT have the same curved surface. The Gaussian curvature of a sphere is $1/r$ and that of the cylinder is $0$. A cylinder can be unrolled onto a plane whereas a sphere cannot (without ripping or stretching).
answered May 10, 2022 at 19:54