Volume of Cone

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:

\(\ds V_K\)

\(=\)

\(\ds \dfrac {V_C} 3\)

\(\ds \)

\(=\)

\(\ds \dfrac {A h} 3\)

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cone
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cone