Correct Answer: $240 \pi$

Solution : Given: The curved surface area of a right circular cone is $156 \pi$ and the radius of its base is 12 cm.
Use the formulas,
The curved surface area of the cone = $\pi rl$,
The volume of the cone = $\frac{1}{3}\pi r^2h$,
The slant height of the cone = $l=\sqrt{r^2+h^2}$,
where $r$, $h$, and $l$ are the radius, height and slant height respectively.
According to the question,
$\pi\times 12\times l=156\pi$
⇒ $l=13$ cm
Also, $l^2=r^2+h^2$
⇒ ${13}^2={12}^2+h^2$
⇒ $169=144+h^2$
⇒ $h^2=169–144$
⇒ $h^2=25$
⇒ $h=5$ cm
The volume of the cone $=\frac{1}{3}\pi\times {12}^2\times 5$
$=12\times 4\times 5\pi =240\pi$ cm ³
Hence, the correct answer is $240 \pi$.