# Capsule (geometry)

A capsule, also known as a stadium of revolution, is a basic three dimensional geometric shape. It consists of a cylinder with hemispherical ends.[1] Another name for this shape is "spherocylinder".[2] The shape is used for containers for pressurised gasses.

## Formulas

The volume of a capsule is calculated by the formula $\pi r^2 \left (\frac{4}{3}r + a \right )$ where $r$ is the radius of the cylinder and hemispheres and $a$ is the length of the cylindrical part.

The surface area formula is $2 \pi r (2r + a)$ where $r$ is the radius of the cylinder and hemispheres and $a$ is the length of the cylindrical part.[3]

## References

1. ^ "Capsule". Mathworld.wolfram.com. 2005-10-20. Retrieved 2013-01-31.
2. ^ Dzubiella, Joachim; Matthias Schmidt, and Hartmut Löwen (2000). "Topological defects in nematic droplets of hard spherocylinders". Physical Review E 62: 5081. doi:10.1103/PhysRevE.62.5081.
3. ^ "Capsule Calculator". Calculatorsoup.com. Retrieved 2013-02-18.