If we imagine the usual children's blocks, it is easy to understand how to find the volume of a cube.Taking the volume of a cube of the cubic volume measure, for example, cubic decimeter, begin to build one large cube.Adding the first square "floor", such as 4x4, you should put another 4 "floor" for all of our edges of the cube are equal.The equality of all sides of the cube - a basic rule, which proves to us that it is a cube.
Find the size of one square face easily, we need only multiply the width and length of the base, that is, to build an edge in the square.Since we have obtained several series - "floors", or rather, their turns in a row an equal amount of an edge of the cube, the resulting square again multiplied by the height of the cube, that is, on its edge.So, in a way that we build an edge in the third degree, in other words - a cube.Just like that, it appears, to find the volume of a cube!
It is from here and takes its name from the construction of the third power - "in a cube."That is, "cubed" should be three times the number multiplied by itself - the expression itself already is based on solution of the problem of finding a cubic volume.
But if the value of the cube edges, that is one side of the cube, is unknown, but given the diagonal of one of its faces, how to find the volume of a cube? Can it be done?It turns out that it is quite computable.
Diagonal party must calculate the direction of the same face value and put it into a cube, that is, in the third degree.To make it clearer, we draw one of the cubic faces - it will be a square, for example, PMNK, where MN - diagonal, which is known to us.Using the Pythagorean theorem, vozvedёm known value of the diagonal in a square or in the second degree.In a right triangle PMN MN side is the hypotenuse, and its square is equal to the sum of the other two sides, erected in the square.
But we know that the legs are - this side of the square face of the cube.Hence, the result must be divided by two and square root.This result will be equal to the side - edges of the cube.Now the question is, how to calculate the volume of a cube, is solved in the simplest way.Just something simply erect side of the cube in the third degree - and the result is obvious.
It often happens that in the problem there is such value as the area of one of the faces of the cube.In this case, you first need to find the side of the square - face of the cube.It is enough to find the square root of a given area.Then, the calculated value is multiplied by the brink of the well-known area.
Sometimes you just need to know how to find the volume of a cube, but there is no size, no ribs, no area of the cube.However, if this task has provided data such as the density and mass, it is possible to calculate the report, multiplying the value of the data density and mass.Seeking volume will be obtained in the product.
And if a person does not contain any measure, what to do in this case?In practice, often use such simple reception, as immersion into the liquid body.So how to find the volume of a cube without tape measures and rulers?
necessary to measure a certain amount of liquid in the tank, for example, in the pan, filling it to the brim.Then the container should be placed in another bowl.Immersing cube in liquid, you should try to collect all the overflow liquid.Then, measuring beaker or its banks (it depends on the volume of a cube), you can make a conclusion about the volume of a cube - it will be equal to the amount of fluid that cube drove his dive.
Unfortunately, it is difficult or even impossible to measure in this way the volume of cubes of considerable size.But since you can learn not only the volume of a cube, but objects of any shape.
There are other possibilities of finding the volume of cubes.For example, for a known length of the diagonal of the cube (not faces!).It is known that the formula is expressed by the product of the diagonal of a cube of his ribs on the square root of 3. Therefore, divide the diagonal of the square root of 3 to obtain the length of the ribs.After that, everything is very simple: to erect a result of the cube and get the desired response.
