Before we move on to the practical part of the article, where we will look for the volume of the parallelepiped, let's remember what kind of figure this is and find out why we need these calculations.
There are three definitions, and all are equivalent. So, the parallelepiped is:
1. A polyhedron having six faces, each of which is a parallelogram.
2. A hexagon that has three pairs of faces parallel to each other.
3. Prism, at the base of which is a parallelogram.
The most common types of the considered geometric figure in our real life are the rectangular parallelepiped and cube. In addition, there are oblique and straight parallelepipeds.
Rectangular box: volume
The rectangular parallelepiped is distinguished by the fact that each face of it is a rectangle. As a household example of this figure, you can bring an ordinary box (shoe, gift, mail).
First you need to find the values of the two sides of the base of the parallelepiped, which are perpendicular to each other (in the plane they would be called width and length).
P = A * B, where A is the length, B is the width.
Now we make one more measurement - the height of the given figure, which we will call N.
Well, we find out the desired volume if we multiply the height by the area of the base, that is:
V = P * N.
The volume of the parallelepiped
The parallelepiped of a straight line is characterized in that its lateral faces are rectangles due to the fact that they are perpendicular to the base of the figure.
The volume is calculated in the same way, the only difference is that the height here is not the edge of the box. In this case, it is a line that connects two opposite faces of the figure and is perpendicular to its base.
Since the base of your box is a parallelogram, not a rectangle, the formula for calculating the area of the base is somewhat complicated. Now it will look like this:
P = A * B * sin (a), where A, B are the length and, accordingly, the width of the base, and “a” is the angle that they form when they intersect.
How to find the volume of a parallelepiped oblique?
Any box that is not straight is recognized as oblique.
Due to the fact that the faces of this figure are not perpendicular to the base, you must first find the height. Multiplying it by the area of the base (see the formula above), you get the volume:
V = P * N, where P is the area of the base, N is the height.
The volume of the box with square faces
A cube is such a rectangular parallelepiped, each of the six faces of which is a square. The property of this figure follows from here - all its edges are equal to each other. As an example, imagine a child’s toy such as cubes.
Well, with finding the volume of the cube, everything is generally extremely simple. To do this, you will need to make only one measurement (ribs) and raise the resulting value to the third degree. Like this:
V = A³.
How can the volume of the box be useful to us in life?
Let's say that you are puzzled by such a problem as the number of boxes that can fit in the trunk of your car. To do this, you need to arm yourself with a ruler or tape measure, pen, sheet of paper, as well as the above formulas for calculating the volume of a rectangular box.
By measuring the volume of one box and multiplying the value by the number of boxes you have, you will find out how many cubic centimeters will be required to place them in the trunk of the car.
And yes, remember that in some cases it will be advisable to convert cubic centimeters to meters. So, if as a result you get a box volume equal to 50 cm in a cube, then for translation just multiply this figure by 0.001. So you get cubic meters. And if you want to know the volume in liters, then multiply the result in cubic meters by 1000.