truncated cone
Definition
Noun: A truncated cone is a geometric solid, or frustum, that results from cutting off the top part of a cone with a plane parallel to its base. It has two parallel circular faces (a smaller top circle and a larger bottom circle) and a curved lateral surface.
Usage
The term is used in geometry, engineering, manufacturing, and everyday descriptions to refer to the shape of an object. * The traffic cone placed on the road is a classic example of a truncated cone. * To calculate the volume of a truncated cone, you need to know the radii of both circular bases and the height. * Many traditional lampshades and certain types of buckets are shaped like a truncated cone.
Advanced Usage
- Mathematical Representation: In technical contexts, a truncated cone is precisely defined as a . Its properties (volume, surface area) are derived from the geometry of a full cone.
- Descriptive Use: The term can be used descriptively outside of strict geometry to characterize any object that tapers smoothly from a wider base to a narrower top with flat, parallel ends.
- The sculptor carved the stone into the form of a truncated cone.
Variants and Related Words
- Frustum (of a cone): The formal geometric term for a truncated cone or pyramid. "Truncated cone" is a specific, more descriptive name for a conical frustum.
- Truncated Pyramid: A related geometric solid formed by cutting off the top of a pyramid with a plane parallel to its base.
Synonyms
- Conical Frustum
- Frustum of a Cone
Related Phrases
- Truncated Shape: A general term for any shape that has had a part, especially an apex or vertex, cut off by a plane.
Noun
- a frustum formed from a cone
