Believe it or not, it's a rectangle. If you strip it away and lay it down flat, it turns into a rectangle.
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It called the curved surface area. There is no special name for it.
A cylinder has 2 equal parallel flat surface circular bases and a curved surface body.
The curved surface are is: pi*diameter*height
it is probably called figure it out, it is curved because glass is sticky. When you measure the volume from a graduated cylinder, measure at the bottom of it. It is called the meniscus.
A sphere has a total curved surface. A cylinder and a cone have a partial curved surface