Volume of Circular Cylinder

Theorem

By Height

Let $\CC$ be a circular cylinder such that:

the bases of $\CC$ are circles of radius $r$

the height of $\CC$ is $h$.

The volume $\VV$ of $\CC$ is given by the formula:

$\VV = \pi r^2 h$

By Slant Height

Let $\CC$ be a circular cylinder such that:

the bases of $\CC$ are circles of radius $r$

the slant height of $\CC$ is $l$

the inclination of the generatrices of $\CC$ to the base of $\CC$ is $\theta$.

The volume $\VV$ of $\CC$ is given by the formula:

$\VV = \pi r^2 l \sin \theta$

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 4$: Geometric Formulas: Circular Cylinder of Radius $r$ and Slant Height $l$
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 7$: Geometric Formulas: Circular Cylinder of Radius $r$ and Slant Height $l$