Volume of Cone

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Theorem

Let $K$ be a cone whose base is of area $A$ and whose height is $h$.

Then the volume of $K$ is given by:

$V_K = \dfrac {A h} 3$


Proof

Let $V_K$ be the volume of $K$.

Let $V_C$ be the volume of a cylinder of base $A$ and of height $h$.

From Volume of Cylinder:

$V_C = A h$

From Volume of Cone is Third of Cylinder on Same Base and of Same Height:

\(\ds V_K\) \(=\) \(\ds \dfrac {V_C} 3\)
\(\ds \) \(=\) \(\ds \dfrac {A h} 3\)

$\blacksquare$