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The dimensions of a rectangular parallelepiped are 2, 3 and 6 cm. Find the length of the edge of such a cube such that the volumes of these bodies are related to their surfaces.
The dimensions of a rectangular parallelepiped are 2 cm, 3 cm and 6 cm. Find the length of the edge of such a cube such that the volumes of these bodies are related to their surfaces.
The dimensions of a rectangular parallelepiped are 2 cm, 3 cm and 6 cm. Find the length of the edge of such a cube such that the volumes of these bodies are related to their surfaces.
The dimensions of a rectangular parallelepiped are 2 cm, 3 cm and 6 cm. Find the length of the edge of such a cube such that the volumes of these bodies are related to their surfaces.
The dimensions of a rectangular parallelepiped are a, by with edge c being its height. Find the angle formed by the diagonal of the parallelepiped with the diagonal of the base that does not intersect it.
The dimensions of a rectangular parallelepiped are 2 cm, 3 cm and 6 cm. Find an edge of a cube such that the volumes of these bodies are related to their surfaces.
These quantities are called cuboid dimensions.
Indeed, the essence of solving the original problem is to establish a relationship connecting four quantities: three dimensions of a rectangular parallelepiped and its diagonal. If three of these four quantities are given, we can find the fourth from the found relationship.
Designations: V - volume, S - base area; S OK - side surface; P - full surface; h - height; a, b, c - measurements of a rectangular parallelepiped; A - apothem of a regular pyramid and a regular truncated pyramid; / - generatrix of the cone; p - perimeter or circumference of the base; r - radius of the base; d - base diameter; R - radius of the ball; D is the diameter of the ball.
Designations: P and Q - perimeter and area of the bases of polyhedra; row - the perimeter and area of the upper base of the truncated pyramid; p and q are the perimeter and area of perpendicular sections of the inclined prism; a, at and H, h - apothems and heights of a regular pyramid and a regular truncated pyramid; I is the length of the inclined prism edge; a, b i c - measurements of a rectangular parallelepiped.
A right parallelepiped whose base is a rectangle is called a cuboid. The lengths of the three edges of a cuboid extending from the same vertex are called the dimensions of the cuboid.
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The dimensions of a parallelepiped are its length, width and height. Here we propose to find them.
Find the dimensions of a rectangular parallelepiped if the areas of the three faces are respectively 30, 48, 40 square cm
There is no need to rummage through all the information about the parallelepiped in search of a solution to this problem. This solution has nothing to do with geometry or the parallelepiped. You need to look at algebra, solving a system of three equations with three unknowns. What does the parallelepiped have to do with it? This is how mathematicians wanted to tie the solution of systems of equations to reality. And, as usual, they missed.
For children's games with numbers, the condition of the problem will do. But for adult mathematics this condition does not work. A not at all childish question immediately arises: how was it possible to determine the areas of the faces of a parallelepiped without knowing its dimensions? After all, we only have rulers to determine length, width, height, distance, size, and so on. No one has yet invented a ruler for measuring areas. And, as I suspect, it is impossible to invent it. These are the mathematical properties of areas. Area we can just calculate knowing the dimensions of a geometric figure. But this is so, a lyrical digression about the quality of the mathematics that we are taught. Let's return to solving the problem.
The area of the face of a parallelepiped is equal to the product of one dimension and another. A rectangular parallelepiped always has three dimensions. Combinations of multiplying two dimensions out of three give us the areas of three different faces. In fact, according to the conditions of the problem, we are given a system of three equations with three unknowns. Let us denote the dimensions of a rectangular parallelepiped by x, y And z. Let's write down our system of equations and solve it using the substitution method.
From the third equation we express z through x. Substitute the resulting value z into the second equation. This gives us the opportunity to express y through x and substitute this value into the first equation. As a result of these simple manipulations, we ended up with one equation with one unknown. Problem for kindergarten. But we got the X squared. We pick out the square root of the number and get the value of X. We can safely discard the negative value, since mathematicians have not yet come up with negative measurements of sizes.
By the way, any mathematical sadist can come up with a negative length and get another academic degree for it. After all, it is only physicists who must confirm their ideas with the results of experiments. Mathematicians just need to come up with a definition. And then we will study negative length in the same way as we study today.
Based on the received value x we can easily find the values y And z. As a result, we got a rectangular parallelepiped with dimensions of 5, 6 and 8 centimeters. By multiplying these numbers, you can easily obtain the areas of the faces of a rectangular parallelepiped, which we know from the condition, from where it is not clear.
In solving the problem of measuring a rectangular parallelepiped, we were helped by:
Here was a link to a site that offered you its services to make your appearance beautiful without any equations. By the way, the surface area of the skin on which beauty is created does not affect the cost of services. Too cumbersome mathematical apparatus will have to be used for these purposes. So it turns out that the cost of beauty does not depend on the geometric area of our body. Thanks to mathematics :)))
And so that the residents of the capital of “all Rus'” did not feel infringed on their rights to beauty, another, of course no less good, beauty salon was offered to their attention. This is even a whole network of salons, so to speak, a mathematical set of salons. You have the opportunity to choose one or another beauty salon depending on the distance to it. Everything is like in real mathematics - each element of a set of salons is matched with elements from a mathematical set of beauties)))
No. 650. The dimensions of a rectangular parallelepiped are 8 cm, 12 cm and 18 cm. Find an edge of a cube whose volume is equal to the volume of this parallelepiped. Given: rectangular parallelepiped. a = 8cm, b = 12cm, c = 8cm Vpar = Vcube Find: d - edge of the cube. Solution: V pair = abc = 8 12 18 = 1728 cm 3. V par = V cube = 1728 cm3 = d3, d 3 = 23 22 3 32 2 = 26 33, d = 12 cm Answer : 12 cm. Home.
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“Solving volume problems”- Vessel. Volume of a part of a cone. A ball is described around a cube with an edge. Square. Volume of one ball. Volume of a cylinder. Attitude. The cylinder is described around the ball. Rectangular parallelepiped. Cone volume. Volume of the ball. Find the volume. Liquid level. Square. Find the volume of part of the cone. Right triangle. The cone is inscribed in the ball.
"Volume of an inclined parallelepiped"- Completed prism. Height. What is volume? Edge. Transformation. Inclined volume. Parallelepipeds and only them have any pair of parallel faces. If a body is divided into parts that are simple bodies, then the volume of this. What is a parallelepiped? Base area. Volume of an inclined parallelepiped.
"Volume of geometric shapes"- Find the volume of the part. Angles. Largest volume. The volume of figures in space. Volume of a cube. Volume of a cube inscribed in a unit dodecahedron. Areas of three faces of a parallelepiped. Volume of the figure. Volumes of two cubes. Find the volume of the cube. Diagonal of a rectangular parallelepiped. Cube Part volume. Volume of a right parallelepiped.
"Volume of an inclined prism"- Volume of bodies. Find the volume of the inclined prism. How to determine the volume of a body if the volume of its parts is known. Property of volumes. Volume of an inclined prism. The volume of an inclined prism is equal to the product of the side edge and the area. The volume of an inclined prism is equal to the product of the area of the base and the height. The base of an inclined prism is a right triangle.
"Calculating the volume of bodies"- Let us recall the volume formula. Volume of a polyhedron. Solve the problem. Find the volume of a rectangular parallelepiped. The volume of a rectangular parallelepiped as a geometric body. Property of volumes. The concept of volume. Equal bodies. Understand the concept of volume. Body. Find the volume of a straight prism. Body volume. Volume of a rectangular parallelepiped.
“How to find the volume of a body”- Aluminum wire. Find the volume of a rectangular parallelepiped. A cubic centimeter is a cube with an edge of 1 cm. The volume of a rectangular parallelepiped. Measurements of a rectangular parallelepiped. If a body is made up of several bodies, then its volume is equal to the sum. Equality of two bodies. Volume of a cube. Find the volume of the cube.
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