Volume 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 volume $\VV$ of $\CC$ is given by the formula:

$\VV = \pi r^2 h$


Proof

From Volume of Cylinder in terms of Height and Base Area:

$\VV = \AA h$

where $\AA$ is the area of the base of $\CC$.


From Area of Circle:

$\AA = \pi r^2$

The result follows.

$\blacksquare$


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 $l$: $4.33$
  • 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 $l$: $7.33.$
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.