solidcone

Solidcone is an informal term used to refer to the three-dimensional geometric solid known as a solid cone. It is formed by all points on straight line segments joining a circular base with a single apex, creating a convex volume bounded by the base circle and a conical surface. In formal geometry, the preferred terms are “solid cone” or “right circular cone,” with solidcone sometimes appearing as a name in non-technical contexts.

In a solid cone, the base has radius r and the perpendicular height from the apex to the base is h. The volume is V = (1/3) π r^2 h. For a right circular cone, the slant height l is sqrt(r^2 + h^2). The lateral surface area is A_l = π r l, and the total surface area is A = π r (r + l). These formulas assume a right circular cone; if the apex is offset from the base center (an oblique cone), the volume formula remains V = (1/3) π r^2 h, but the lateral surface area typically does not simplify to a single simple expression.

A related shape is the truncated cone, or frustum, obtained by slicing a cone with a plane parallel to the base. Cones have appeared in various fields, including mathematics, architecture, and engineering, and also in everyday objects such as ice cream cones and funnels. In computer graphics and CAD, cone primitives are common building blocks for modeling, rendering, and simulations.

The term cone derives from Latin conus, which itself comes from the Greek konos, reflecting the historical study of this shape. Solidcone, when encountered, is usually a nonstandard shorthand for the solid cone and is best understood in context.