Before we turn to the practical part of the article, where we will look for the volume of a parallelepiped, let's remember what kind of figure this is, and we will find out why these calculations may be necessary for us.
There are three definitions, and they are all equivalent. So, the parallelepiped is:
1. A polyhedron with six faces, each of which is a parallelogram.
2. Hexagon, which has three pairs of faces parallel to each other.
3. Prism, in the base of which there is a parallelogram.
The most common types of the geometrical figure in our real life are the rectangular parallelepiped and the cube. In addition, distinguish between an inclined and a straight parallelepiped.
Rectangular parallelepiped: volume
A 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, postal).
To begin with, it is necessary to find the values of the two sides of the base of the parallelepiped, which are perpendicular to each other (on the plane they would be called the 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 H.
Well, we find out the required volume if we multiply the height by the area of the base, that is:
V = П * Н.
The volume of a straight parallelepiped
The parallelepiped is directly distinguished by the fact that its lateral faces are rectangles because they are perpendicular to the bases of the figure.
The volume is calculated similarly, the only difference is,that the height here is not an edge of a parallelepiped. In this case, it is a line that connects the two opposite faces of the figure and is perpendicular to its base.
Since the base of your parallelepiped is a parallelogram, and not a rectangle, then the formula for calculating the base area becomes somewhat more complicated. Now it will look like this:
P = A * B * sin (a), where A, B is the length and, respectively, the width of the base, and "a" is the angle they form at their intersection.
How to find the volume of a parallelepiped oblique?
An inclined is recognized as any parallelepiped, which is not a straight line.
Due to the fact that the faces of this figure are not perpendicular to the base, you first need to find the height. Multiplying it by the area of the base (see the formula above), you will get the volume:
V = П * Н, where П - the area of the base, Н - height.
The volume of a box with square faces
A cube is a rectangular parallelepiped,each of the six faces of which is a square. This implies the property of this figure - all its edges are equal. As an example, imagine a child's toy, like cubes.
Well, finding the volume of a cube is generally very simple. To do this, you only need to produce one dimension (edges) and raise the resulting value to the third power. Like this:
V = A³.
How can the volume of the parallelepiped be useful to us in life?
Let's say that you are puzzled by such a problem asnumber of boxes that can be placed in the trunk of your car. To do this, you need to arm yourself with a ruler or a tape measure, a pen, a sheet of paper, as well as the above formulas for calculating the volume of a rectangular box.
Measuring the volume of one box and multiplying the value by the number of boxes you have, you will learn how many cubic centimeters it will take for them to be placed in the trunk of the car.
And yes, remember that in some cases, cubiccentimeters would be advisable to translate into meters. So if as a result you got 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, multiply the result in cubic meters by 1000.