What is the cube, and what it has diagonal
Cube (regular polyhedron or hexahedron) is a three-dimensional figure, each face - a square, which, as we know, all sides are equal.Diagonal of a cube is the segment that passes through the center of the figure and connect symmetrical peaks.In the right hexahedron has four diagonally, and they are equal.It is important not to confuse the diagonal of the figure with a diagonal of her face or square, which lies at its base.Diagonal of the cube through the center and connects the edge opposite the top of the square.
formula, which can be found on the diagonal of a cube
Diagonal regular polyhedron can be found on a very simple formula that you want to remember.D = a√3, where D is a diagonal of a cube, and - this is the edge.Here is an example of the problem, where you need to find a diagonal, it is known that the length of its edge is 2 cm. It's simple D = 2√3, even considered as nothing.In the second example, let the edge of the cube is equal to √3 see, then we get D = √3√3 = √9 = 3.Answer: D is 3 cm.
formula, which can be found on the diagonal of the cube
diagonal facets can also be found by the formula.Diagonals who are on the verge of a total of 12 units, and they are all equal.Now we remember d = a√2, where d - is the diagonal of a square, and - this is also an edge of a cube or a side of the square.To understand where this formula is very simple.After all, two sides of a square and the diagonal to form a right triangle.This trio plays the role of the hypotenuse of the diagonal and the sides of a square - the legs of it, which have the same length.Let us remember the Pythagorean theorem, and all at once will fall into place.Now the problem: edge hexahedron equal √8 see, you need to find a diagonal of its faces.We put in the formula, and we get d = √8 √2 = √16 = 4.Answer: The diagonal of the cube is 4 cm.
If you know the diagonal of the cube
According to the problem, we are given only the diagonal faces of a regular polyhedron, that is, suppose, √2 cm, and we need to find a diagonal of a cube.The formula of this task a little more difficult the last.If we know d, then we can find the edge of the cube, on the basis of our second formula d = a√2.We get a = d / √2 = √2 / √2 = 1cm (this is our edge).If this value is known, then to find the diagonal of a cube is not difficult: D = 1√3 = √3.That's how we solved our task.
If you know the surface area
following algorithm is based on finding solutions diagonally over the surface area of the cube.Assume that it is equal to 72 cm2.To begin with we find the area of one face, and a total of 6. So, you need to divide 72 by 6 and get 12 cm2.This is one area of the face.To find the edge of a regular polyhedron, it is necessary to recall the formula S = a2, then a = √S.Substitute and get a = √12 (edge of the cube).And if we know this value, and not difficult to find a diagonal D = a√3 = √12 √3 = √36 = 6. Answer: The diagonal of a cube is 6 cm2.
If you know the length of the edges of the cube
There are cases when the task is given only the length of the edges of the cube.Then, this value must be divided by 12. That's how much the parties in the regular polyhedra.For example, if the sum of all the ribs is 40, one side is equal to 40/12 = 3.333.We put in our first formula and get the answer!
