Does a cylinder have to be open or can they be closed in?

Answer 1

In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates:


This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). Even more general is the generalized cylinder: the cross-section can be any curve.

The cylinder is a degenerate quadric because at least one of the coordinates (in this case z) does not appear in the equation. By some definitions the cylinder is not considered to be a quadric at all.

In common usage, a cylinder is taken to mean a finite section of a right circular cylinder with its ends closed to form two circular surfaces, as in the figure (right). If the cylinder has a radius r and length (height) h, then its volume is given by


and its surface area is


For a given volume, the cylinder with the smallest surface area has h = 2r. For a given surface area, the cylinder with the largest volume has h = 2r, i.e. the cylinder fits in a cube (height = diameter.)

There are other more unusual types of cylinders. These are the imaginary elliptic cylinders:


the hyperbolic cylinder:


and the parabolic cylinder:

Answer 2

Either

A tin can is a cylinder whether it's closed or open.

A rolling pin is also a cylinder, as it a broomstick.

Answer 3

either 1