We are given:
- Circumference of circle $\(\mathrm{C} 1=12 \pi\)$
- Circumference of circle $\(\mathrm{C} 2=48 \pi\)$

The formula for circumference is:

$$
\(C=2 \pi r\)
$$

where $r$ is the radius.
From the circumferences, we can find the radii:
For C1:

$$
\(12 \pi=2 \pi r_1 \Longrightarrow r_1=\frac{12 \pi}{2 \pi}=6\)
$$


For C2:

$$
\(48 \pi=2 \pi r_2 \Longrightarrow r_2=\frac{48 \pi}{2 \pi}=24\)
$$


Next, the area $A$ of a circle is:

$$
\(A=\pi r^2\)
$$


So,

$$
\(\begin{gathered}
A_1=\pi(6)^2=36 \pi \\
A_2=\pi(24)^2=576 \pi
\end{gathered}\)
$$


The ratio of the areas $\(\frac{A_2}{A_1}\)$ is:

$$
\(\frac{576 \pi}{36 \pi}=\frac{576}{36}=16\)
$$


Thus, the ratio of the area of $C_2$ to $C_1$ is 16 to 1 .
Answer: (e) 16 to 1.