Lateral Surface Area of Circular Cylinder

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 $

$=$

$\ds 2 \pi r h \cosec \theta$

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

$\AA = 2 \pi r l$

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 $l$