Volume of Cylinder/Mistake/First Edition

Source Work

1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables:

Chapter $4$: Geometric Formulas
Cylinder of Cross-sectional Area $A$ and Slant Height $l$


Mistake

$4.35. \quad$ Volume $= A l = \dfrac {A h} {\sin \theta} = A h \csc \theta$
$4.36. \quad$ Lateral surface area $= p l = \dfrac {p h} {\sin \theta} = p h \csc \theta$


Correction

The formulae quoted are indeed for the cylinder whose cross-section is of area $A$.

However, the accompanying diagram illustrates the area of the base, not the cross-section.


Also, $p$ needs to be explicitly specified as being the perimeter of the cross-section.

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

Lack of clarity and confusion are likely outcomes.


Also see


Sources

  • 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 $l$
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