Capsule (geometry)

A capsule (from Latin capsula, "small box or chest"), or stadium of revolution, is a basic three-dimensional geometric shape consisting of a cylinder with hemispherical ends.[1] Another name for this shape is spherocylinder.[2]

A two-dimensional orthographic projection of a capsule

The shape is used for containers for pressurised gases and for pharmaceutical capsules.

Formulas

a is the letter used for cylindrical height here

The volume of a capsule is calculated by adding the volume of the two hemispheres (a sphere of radius $r$ ) to the volume of the cylindrical part: ${\textstyle V={\frac {4}{3}}\pi r^{3}+(\pi r^{2}a)}$

This simplifies to the formula $V=\pi r^{2}\left({\frac {4}{3}}r+a\right)$ .

The surface area formula is $C=2\pi r(2r+a)$ .[3]

References

Weisstein, Eric W. "Capsule". MathWorld.
Dzubiella, Joachim; Matthias Schmidt; Hartmut Löwen (2000). "Topological defects in nematic droplets of hard spherocylinders". Physical Review E. 62: 5081. arXiv:cond-mat/9906388. Bibcode:2000PhRvE..62.5081D. doi:10.1103/PhysRevE.62.5081.
"Capsule Calculator". Calculatorsoup.com. Retrieved 2013-02-18.

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[1] Weisstein, Eric W. "Capsule". MathWorld.

[2] Dzubiella, Joachim; Matthias Schmidt; Hartmut Löwen (2000). "Topological defects in nematic droplets of hard spherocylinders". Physical Review E. 62: 5081. arXiv:cond-mat/9906388. Bibcode:2000PhRvE..62.5081D. doi:10.1103/PhysRevE.62.5081.

[3] "Capsule Calculator". Calculatorsoup.com. Retrieved 2013-02-18.