To determine the total volume of water that a pack of 12 conical cups can hold, we first need to find the volume of a single cone. The formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.
Given:
- Radius \( r = 7 \) centimeters
- Height \( h = 12 \) centimeters
- Approximate \(\pi \) is given as \( 3.14 \)
Now we can calculate the volume of one cup:
\[ V = \frac{1}{3} \times 3.14 \times (7^2) \times 12 \]
Calculating \( 7^2 \):
\[ 7^2 = 49 \]
Now substitute \( 49 \) back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]
Now, calculate \( 49 \times 12 \):
\[ 49 \times 12 = 588 \]
Now substitute \( 588 \) into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 588 \]
Next, calculate \( 3.14 \times 588 \):
\[ 3.14 \times 588 = 1847.92 \]
Now, we calculate \( \frac{1}{3} \times 1847.92 \):
\[ V = \frac{1847.92}{3} = 616.64 \]
Thus, the volume of one cup is \( 616.64 \) cubic centimeters.
Now to find the volume of a pack of 12 cups, we multiply the volume of one cup by 12:
\[ \text{Total Volume} = 616.64 \times 12 \]
Calculating this gives:
\[ \text{Total Volume} = 7399.68 \]
Therefore, the total volume of water that a pack of 12 cups will hold is
\[ \boxed{7399.68} \text{ cubic centimeters.} \]