Volume of Cylinder/Slant Height and Base Area

Theorem

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:

$\VV = A l \sin \theta$


Proof


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Sources

  • 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 $l$: $7.35.$
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