Volume of Cylinder/Height and Cross-Sectional Area

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:

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


Proof


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Sources

  • 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 $l$: $4.35$
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