To find the volume of the hexagonal prism labeled "Choosy Cheesy," we can use the formula for the volume of a prism, which is given by:
\[ V = B \cdot h \]
where \(B\) is the area of the base, and \(h\) is the height of the prism.
Step 1: Calculate the area of the hexagonal base.
Given that the two parallel sides of the hexagonal prism each measure 30 centimeters in length, it suggests that we are dealing with a regular hexagonal prism. The area \(A\) of a regular hexagon can be calculated using the formula:
\[ A = \frac{3\sqrt{3}}{2} \cdot s^2 \]
where \(s\) is the length of a side.
However, from the problem, we interpret that given the parallel sides are 30 cm, we can find the side length \(s\) of the hexagon. In a regular hexagon, the relationship between the side length and the longer parallel side (which corresponds to the diameter of the hexagon across its width) is \(s \cdot \sqrt{3} = 30\), which means:
\[ s = \frac{30}{\sqrt{3}} = 10\sqrt{3} \text{ centimeters} \]
Next, we calculate the area \(A\) of the hexagon using the derived side length:
\[ A = \frac{3\sqrt{3}}{2} \cdot (10\sqrt{3})^2 \] \[ A = \frac{3\sqrt{3}}{2} \cdot 300 \] \[ A = 450\sqrt{3} \text{ square centimeters} \]
Step 2: Calculate the height of the prism.
The height \(h\) of the hexagonal prism is provided as 8 centimeters.
Step 3: Calculate the volume.
Finally, we can calculate the volume \(V\) of the prism by substituting our values into the volume formula:
\[ V = A \cdot h = (450\sqrt{3}) \cdot 8 \] \[ V = 3600\sqrt{3} \text{ cubic centimeters} \]
Thus, the volume of the box is:
\[ \boxed{3600\sqrt{3}} \text{ cubic centimeters} \]
This volume represents the total capacity of the gourmet cheese box.