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A rectangular parallelepiped is a body all of whose faces are rectangles. Parallelos, translated from ancient Greek, literally means “walking side by side”, epidos - “flatness”.
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The figure shows various geometric bodies. Name those that can be images of a rectangular parallelepiped.
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A rectangular parallelepiped has dimensions - length, width and height. The dimensions of a cuboid are the lengths of the three edges emanating from one vertex.
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Volume of a rectangular parallelepiped Volume is a number that shows how many cubes with an edge equal to a unit of length (measures of volume) can be placed inside the figure. The number of all cubes with a side of 1 cm into which a rectangular parallelepiped can be cut is its volume, expressed in cubic centimeters. If a, b and c are the dimensions of a rectangular parallelepiped, then its volume V is found by the formula V = a b c. If we omit the multiplication signs, then this formula can be written as follows: V = abc.
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Think about the problem: A corner has been cut off from a cube. How many faces does the resulting polyhedron have? What shape do they have? How many vertices and edges does a polyhedron have?
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Problem about a fly. The picture shows a transparent cube. On the surface of this cube there is a spider, which gazes through it at a fly sitting on the other side of the cube. In order to catch a fly, the spider needs to get to it as quickly as possible. In other words, the spider needs to move towards it along the shortest path.
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In order to understand which path the spider should move towards the fly, you need to mentally bend the side face of the cube on which the spider sits and place the top and side faces in the same plane.
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If you look at these edges from above, we get what is shown in the figure: the edges on which the spider and the fly sit. Now the shortest path is easy to find - this is the segment RM. RM - geodetic line - a line that in the drawing shows the shortest path from one point to another.
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Development of a rectangular parallelepiped The figure that is obtained when a polyhedron is fully developed is called a development
9. How many edges does a rectangular parallelepiped have? Answer: 12 edges 10. How many vertices does a cuboid have? Answer: 8 vertices 11. How many faces does a rectangular parallelepiped have? Answer: 6 faces 12. Is a cube a rectangular parallelepiped? Answer: Yes. Back.
Picture 9 from the presentation “Blitz survey” for mathematics lessons on the topic “Games in mathematics”Dimensions: 960 x 720 pixels, format: jpg. To download a free picture for a math lesson, right-click on the image and click “Save image as...”. To display pictures in the lesson, you can also download the entire presentation “Blitz survey.pptx” with all the pictures in a zip archive for free. The archive size is 61 KB.
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“Competition in mathematics” - KVN in mathematics. Team “Plus” Team “Minus” 9-2= 8+2= 4+5= 10-1= 2+6= 7-5= 7-3= 10-4= 9-5= 9+0= 8- 5= 2+6= 4+4= 6-2= 3+7= 9-7= 3+4= 8+2=. Greetings from the teams. Physical education minute. Team "Plus" Team "Minus". Verbal counting. And they disappeared behind the bushes. Warm up. Team “Plus” 7 2 1 2 4 6 10 2 = 2 Team “Minus” 8 1 5 3 6 3 10 2 = 2.
“Mathematics Games” - Play is one of the most important means of mental and moral education of children. Objectives: Monitoring learning in mathematics. Work experience on the topic “The role of games in teaching mathematics.” Objectives: Relevance: S.T.Shatsky. “The role of games in the learning process in mathematics lessons.”
“Blitz survey” - K, Plato. M, Sonya. D, Katya. B, Matvey. P.I., Philip. Repetition. B, Nikita. Kolya.
“Mathematics in Games” - I want you to tell me: How many goodies were there? 7 buns. Creative work in mathematics by 7th grade A student Artur Grekov. With an empty wallet, alas! Board logic game - chess. It got dark. Moscow 2010 Zaitsev N.A. - author of the famous textbook “Zaitsev’s Cubes”. Pascal. Mathematics in games.
“Barsik the cat” - I measured the length of Barsik’s jump. Antoine de Saint-Exupery. I wondered how much water a cat drinks. The average speed at which a cat runs after a candy wrapper is 6 km/h. We often photograph Barsik. The average speed at which a cat meets dad is 3 km/h. I calculated the average speed at which Barsik moves around the apartment.
“Didactic games in mathematics” - X · y = ? Target. Instilling an interest in mathematics. Completed by a teacher of secondary school No. 2 r.p. Dergachi Shkodina S.A. 12 stream, group No. 3. Formation of skills and abilities in the process of didactic games. Didactic games in mathematics lessons.
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The prism is called parallelepiped, if its bases are parallelograms. Cm. Fig.1.
Properties of a parallelepiped:
The opposite faces of a parallelepiped are parallel (that is, they lie in parallel planes) and equal.
The diagonals of a parallelepiped intersect at one point and are bisected by this point.
Adjacent faces of a parallelepiped– two faces that have a common edge.
Opposite faces of a parallelepiped– faces that do not have common edges.
Opposite vertices of a parallelepiped– two vertices that do not belong to the same face.
Diagonal of a parallelepiped– a segment that connects opposite vertices.
If the lateral edges are perpendicular to the planes of the bases, then the parallelepiped is called direct.
A right parallelepiped whose bases are rectangles is called rectangular. A prism, all of whose faces are squares, is called cube.
Parallelepiped- a prism whose bases are parallelograms.
Right parallelepiped- a parallelepiped whose lateral edges are perpendicular to the plane of the base.
Rectangular parallelepiped is a right parallelepiped whose bases are rectangles.
Cube– a rectangular parallelepiped with equal edges.
parallelepiped called a prism whose base is a parallelogram; Thus, a parallelepiped has six faces and all of them are parallelograms.
Opposite faces are pairwise equal and parallel. The parallelepiped has four diagonals; they all intersect at one point and are divided in half at it. Any face can be taken as a base; the volume is equal to the product of the area of the base and the height: V = Sh.
A parallelepiped whose four lateral faces are rectangles is called a straight parallelepiped.
A right parallelepiped whose six faces are rectangles is called rectangular. Cm. Fig.2.
The volume (V) of a right parallelepiped is equal to the product of the base area (S) and the height (h): V = Sh .
For a rectangular parallelepiped, in addition, the formula holds V=abc, where a,b,c are edges.
The diagonal (d) of a rectangular parallelepiped is related to its edges by the relation d 2 = a 2 + b 2 + c 2 .
Rectangular parallelepiped- a parallelepiped whose side edges are perpendicular to the bases, and the bases are rectangles.
Properties of a rectangular parallelepiped:
In a rectangular parallelepiped, all six faces are rectangles.
All dihedral angles of a rectangular parallelepiped are right.
The square of the diagonal of a rectangular parallelepiped is equal to the sum of the squares of its three dimensions (the lengths of three edges that have a common vertex).
The diagonals of a rectangular parallelepiped are equal.
A rectangular parallelepiped, all of whose faces are squares, is called a cube. All edges of the cube are equal; the volume (V) of a cube is expressed by the formula V=a 3, where a is the edge of the cube.
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