The volume of a cone of radius $12cm$ and slant height $20cm$ is $16896c{m}^3$.

The correct option is B

False

Volume of a cone or radius $r$ and height $h$ is $\frac{1}{3}\pi r^{2}h$

In the cone shown above, radius, $r=BC=12cm$

Slant height, $l=AC=20cm$

Height, $h=AB$

In $△ABC$,

$l^2+h^2+r^2$

$\Rightarrow {20}^2=h^2+{12}^2$

$\Rightarrow h^2={20}^2-{12}^2$

$\Rightarrow h=\sqrt{{20}^2-{12}^2}=\sqrt{256}=16cm$
Now, volume of the Cone$=\frac{1}{3}\times \pi \times r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times {12}^2\times 16$
$=\frac{16896}{7}c{m}^3$

Hence, the given statement is false.