Volume of Cylinder

Theorem

Let $\CC$ be a cylinder such that:

the cross-sections of $\CC$ at right angles to the generatrices of $\CC$ have area $A$

the height of $\CC$ is $h$

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

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

$\VV = \dfrac {A h} {\sin \theta} = A h \csc \theta$

Let $\CC$ be a cylinder such that:

the cross-sections of $\CC$ at right angles to the generatrices of $\CC$ have area $A$

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

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

$\VV = A l$

Let $\CC$ be a cylinder such that:

the bases of $\CC$ have area $A$

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

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

$\VV = A h$

Let $\CC$ be a cylinder such that:

the bases of $\CC$ have area $A$

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:

$\VV = A l \sin \theta$

1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 4$: Geometric Formulas: Cylinder of Cross-sectional Area $A$ 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: Cylinder of Cross-sectional Area $A$ and Slant Height $l$