Before we move on to the practical part of the article, where the volume of the box we seek, let us remember what the figure of this and find out why these calculations we might need.
There are three definitions, all of them are equivalent.For example, a parallelepiped:
1. A polyhedron with six faces, each of which is a parallelogram.
2. Hex, which has three pairs of faces parallel with each other.
3. prism whose base is a parallelogram.
Most probably common in our real life types under consideration of geometric shapes - a cuboid and the cube.In addition, the distinction is made between direct and oblique parallelepiped.
a cuboid: Volume
a cuboid different is that each facet of his - a rectangle.As a household example of this figure can lead a normal box (a shoe, gift, postage).
First we need to find the values of the two sides of the base of the parallelepiped, which are arranged perpendicular to one another (in the plane they called width and length).
P = A * B, where A - length B - width.
Now make another dimension - the height of a given shape, which we call the N.
Well, we know the required amount by multiplying the height of the square base, ie:
V = P * N.
volume of the box directly
straight parallelepiped characterized in that the side of its facets - rectangles due to the fact that they are perpendicular to the base figure.
volume is calculated similarly, the only difference is that the height here - not the edge of the box.In this case it is a line that connects two opposing faces perpendicular to the figure and its base.
Since your base parallelepiped is a parallelogram, not a rectangle, then the formula for calculating the area of the base is somewhat complicated.Now she looks in this way:
P = A * B * sin (a), where A, B - length and, accordingly, the width of the base, and the "a" - the angle that they form at their intersection.
How to find the volume of a parallelepiped inclined?
recognized any tilt a box that is not right.
Owing to this shape that the faces are not perpendicular to the base, first find the height.Multiplying it on the same area of the base (see above formula), and you get the volume:
V = P * N, where P - base area, H - height.
volume parallelepiped with square faces
Cube - is a cuboid, each of the six faces of which is a square.Hence the shape of the property - all its edges are equal among themselves.As an example, imagine a child's toy as cubes.
Well, finding the volume of a cube all generally very simple.To do this, you will need to make only one dimension (rib) and build the value obtained in the third degree.So:
V = A³.
How can the volume of the box can be useful to us in our lives?
assume that you are puzzled such a problem, as the number of boxes that can be accommodated in the trunk of your car.To do this, you need to arm themselves with a ruler or tape measure, pen, a sheet of paper, as well as the above formulas for calculating the volume of a cuboid.
measure the volume of a box, and multiplying the value by the number of boxes available to you, you will know how many cubic centimeters is required to be stored in the trunk of the car.
And yes, remember that in some cases it is advisable to cubic centimeters will be converted into meters.So, if as a result you get the volume of a box of 50 cm cube, then transfer just multiply this figure by 0,001.So you get a cubic meter.And if you want to know the volume in liters, the result in cubic meters multiply by 1000.