Volume of Cylinder/Mistake/Third Edition

Source Work

2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.):

Chapter $7$: Geometric Formulas
Cylinder of Cross-sectional Area $A$ and Slant Height $l$


Mistake

$7.35. \quad$ Volume $= A h = A l \sin \theta$
$7.36. \quad$ Lateral surface area $= p h = p l \sin \theta$


Correction

The formulae quoted are for the cylinder whose bases are of area $A$.

However, the title states that they are for the cross-section.


Also, $p$ needs to be explicitly specified as being the perimeter of the base.

This has been left implicit from the accompanying diagram, which does in fact appear to illustrate $p$ as being the perimeter of the base.

Lack of clarity and confusion are likely outcomes.


Also see


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 $l$
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