A cylinder is a three-dimensional geometric shape with two parallel circular bases connected by a curved surface. It is defined by:
\[ V = \frac{\pi r^2 h}{3} \]
This formula calculates the volume of a cylinder, which is the space enclosed by the curved surface and two bases. It is derived by multiplying the area of the base (\(\pi r^2\)) by the height of the cylinder.
\[ A = \pi r s \]
This formula calculates the lateral surface area, which is the area of the curved surface excluding the two bases. The term \(s\) is the slant height, which can be found using the Pythagorean theorem in case of a slanted cylinder.