Lateral Surface Area of Circular Cylinder/Height

Theorem

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

the bases of $\CC$ are circles of radius $r$
the height of $\CC$ is $h$
the inclination of the generatrices of $\CC$ to the base of $\CC$ is $\theta$.


The area $\AA$ of the lateral surface of $\CC$ is given by the formula:

\(\ds \AA\) \(=\) \(\ds \dfrac {2 \pi r h} {\sin \theta}\)
\(\ds \) \(=\) \(\ds 2 \pi r h \cosec \theta\)


Proof


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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 $l$: $4.34$
  • 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 $l$: $7.34.$
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