# How does a hemisphere's curved surface look unfolded?

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.

• A cylinder is flat (curvature 0), so can be unrolled to a piece of paper. A hemisphere is curved, so cannot. Commented May 10, 2022 at 19:34
• Not a duplicate, but probably of interest: math.stackexchange.com/questions/4345667/… Commented May 10, 2022 at 20:13
• see what happens when you peel off half an orange, and then try to flatten it. it will crack. Commented May 10, 2022 at 20:15

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).