Lateral Surface Area of Cylinder

Theorem

Let $\CC$ be a cylinder such that:

the perimeter of a cross-section of $\CC$ at right angles to the generatrices is $p$

the height of $\CC$ is $l$

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:

$\AA = \dfrac {p h} {\sin \theta} = p h \cosec \theta$

Let $\CC$ be a cylinder such that:

the perimeter of a cross-section of $\CC$ at right angles to the generatrices is $p$

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

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

$\AA = p l$

Let $\CC$ be a cylinder such that:

the perimeter of the bases of $\CC$ is $p$

the height of $\CC$ is $h$

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

$\AA = p h$

Let $\CC$ be a cylinder such that:

the perimeter of the base of $\CC$ is $p$

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

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:

$\AA = p l \sin \theta$

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 $l$