The formula to calculate the volume of a hexagonal prism is:
\[ V = \frac{3\sqrt{3} \cdot a^2 \cdot h}{2} \]
where \( V \) is the volume, \( a \) is the length of the side of the hexagon, and \( h \) is the height of the hexagonal prism.
A hexagonal volume refers to the three-dimensional space that a hexagonal prism occupies. A hexagonal prism is a geometric shape that has two hexagonal bases and six rectangular sides. The volume of a hexagonal prism can be calculated using the formula: \( V = Bh \), where \( B \) is the area of the base and \( h \) is the height of the prism. The base area (\( B \)) of a hexagon can be found using the formula: \( B = \frac{3}{2} \sqrt{3} s^2 \), where \( s \) is the length of a side of the hexagon. Therefore, the volume of a hexagonal prism is the product of the height and the area of the hexagonal base. This concept is used in various fields such as architecture, engineering, and mathematics.
Let's assume we have the following values:
Step 1: Calculate the square of the length of the side:
\[ a^2 = 4^2 = 16 \]
Step 2: Multiply the result by the height and \( 3\sqrt{3} \):
\[ 3\sqrt{3} \cdot 16 \cdot 10 = 480\sqrt{3} \]
Step 3: Divide the result by 2:
\[ \frac{480\sqrt{3}}{2} = 240\sqrt{3} \]
Therefore, the volume of the hexagonal prism is \( V = 240\sqrt{3} \) cubic units.
