The formula to calculate the Volume of a Parallelepiped is:
\[ V = l \cdot w \cdot h \]
Where:
A volume of a parallelepiped is a measure of the three-dimensional space enclosed by a parallelepiped. A parallelepiped is a three-dimensional figure formed by six parallelograms. The volume of a parallelepiped can be calculated by finding the scalar triple product of the three vectors forming the parallelepiped. This is done by taking the dot product of one of the vectors with the cross product of the other two vectors. The result is a scalar quantity that represents the volume of the parallelepiped. The volume can also be found by multiplying the area of the base by the height, similar to finding the volume of a prism. The volume of a parallelepiped gives the capacity of the shape and is usually measured in cubic units.
Let's consider an example:
Using the formula to calculate the Volume of a Parallelepiped:
\[ V = 5 \times 3 \times 4 = 60 \, \text{m}^3 \]
This demonstrates that with a length of 5 meters, a width of 3 meters, and a height of 4 meters, the volume of the parallelepiped would be 60 m³.