Capsule (geometry)

A capsule (from

It can also be referred to as an oval although the sides (either vertical or horizontal) are straight parallel.

The shape is used for some objects like containers for pressurised gases, building domes, and pharmaceutical capsules.

In chemistry and physics, this shape is used as a basic model for non-spherical particles. It appears, in particular as a model for the molecules in liquid crystals^[6][3][4] or for the particles in granular matter.^[5][7][8]

The volume ${\displaystyle V}$ of a capsule is calculated by adding the volume of a ball of radius ${\displaystyle r}$ (that accounts for the two hemispheres) to the volume of the cylindrical part. Hence, if the cylinder has height ${\displaystyle h}$,

${\displaystyle V={\frac {4}{3}}\pi r^{3}+(\pi r^{2}h)=\pi r^{2}\left({\frac {4}{3}}r+h\right)}$.

The surface area of a capsule of radius ${\displaystyle r}$ whose cylinder part has height ${\displaystyle h}$ is ${\displaystyle 2\pi r(2r+h)}$.

A capsule can be equivalently described as the

of a ball of radius ${\displaystyle r}$ with a line segment of length ${\displaystyle a}$.^[5] By this description, capsules can be straightforwardly generalized as Minkowski sums of a ball with a polyhedron. The resulting shape is called a spheropolyhedron.^[7][8]

A capsule is the three-dimensional shape obtained by revolving the two-dimensional

.

References

This elementary geometry-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e