To find the volume of the hexagonal prism, we will use the formula for the volume of a prism:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
Step 1: Find the base area of the hexagon.
The hexagonal prism can be divided into two types of triangles forming the hexagon. Given that the longer parallel sides of the hexagon measure 30 cm, it suggests that we're dealing with a regular hexagon or a suitable approximation where the sides are equal.
For a regular hexagon with side length \( s \):
- The area of a regular hexagon can be calculated using the formula:
\[ \text{Area} = \frac{3\sqrt{3}}{2}s^2 \]
However, we don't have the side length directly, but we can use the relationship of the hexagon's dimensions to deduce it.
Given that the two longer parallel sides are 30 cm, this means:
\[ s = \frac{30}{\sqrt{3}} \approx 17.32 \text{ cm} \]
Step 2: Calculate the area of the hexagonal base.
The area of the hexagon with side length \( s = \frac{30}{\sqrt{3}} \) can be calculated as follows:
\[ \text{Area} = \frac{3\sqrt{3}}{2}\left(\frac{30}{\sqrt{3}}\right)^2 = \frac{3\sqrt{3}}{2} \cdot \frac{900}{3} = 150\sqrt{3} \text{ cm}^2 \approx 259.81 \text{ cm}^2 \]
Step 3: Calculate the height of the prism.
The given height of the prism is 8 cm.
Step 4: Calculate the volume of the hexagonal prism.
Now we can substitute the area of the base and the height into the volume formula:
\[ \text{Volume} = 150\sqrt{3} \times 8 = 1200\sqrt{3} \text{ cm}^3 \approx 2078.46 \text{ cm}^3 \]
Thus, the volume of the box is approximately 2078.46 cubic centimeters.