Cylinder

Topic

3D Geometry

Definition

A cylinder is a three-dimensional geometric figure with two parallel circular bases connected by a curved surface at a fixed distance from each other.

Description

In the realm of three-dimensional geometry, a cylinder is a fundamental shape characterized by its two identical, parallel circular bases and a curved surface that connects these bases. The line segment joining the centers of the bases is called the axis of the cylinder, and it is perpendicular to the bases. The distance between the bases is the height of the cylinder, while the radius is the distance from the center to the edge of the base.

Cylinders are prevalent in various real-life applications and are essential in fields such as engineering, architecture, and manufacturing. For instance, cylinders are used in the design of pipes, tanks, and even everyday objects like cans and batteries. Understanding the properties of cylinders, such as their volume and surface area, is crucial for optimizing material usage and structural integrity in construction and design projects.

In mathematics, cylinders are studied not only for their practical applications but also for their theoretical properties. They serve as a basis for understanding more complex shapes and forms in three-dimensional space. The volume of a cylinder is calculated using this formula $$ V = \pi r^2 h $$where r is the radius of the base and h is the height. The surface area is given by this formula $$ A = 2\pi r(h + r) $$which includes the areas of the two bases and the curved surface.

For a complete collection of terms related to 3D geometry click on this link: 3D Collection.