Tisch
Knowledge point 1. Features of a cuboid: there are 6 faces, and the opposite faces are exactly the same; There are 12 sides, and the sides are equal in length; There are eight vertices
2. The characteristics of the cube: the six faces of the cube are exactly the same; 12 sides are all equal in length; There are eight vertices.
3. The meaning of length, width and height of rectangle: the length of three sides intersecting at the same vertex is called the length, width and height of cuboid respectively.
The surface areas of cuboids and cubes are 1. Meaning of surface area: The total area of six or five faces of a cuboid or cube is called its surface area.
2. Calculation method of cuboid surface area: (2)
3. Calculation method of cubic surface area: cubic surface area = side length 2×6.
The volume of cuboids and cubes is 1. Significance of volume: The size of the space occupied by an object is called volume.
2. unit of volume: cubic meters, cubic decimeters and cubic centimeters; Letters: m3, dm3, cm3.
3. Propulsion rate per unit volume:1m3 =1000 dm3dm3 =1000 cm3.
4. Meaning of volume: the volume of a box, oil drum, etc. What can hold an object is called the volume of the box.
5. The propulsion rate between unit of volume: 1L= 1000ml.
6. Conversion between unit of volume and unit of volume: 1L = dm3 1cm3. = 1 ml.
7. Cuboid volume calculation formula and cube volume calculation formula.
8. Volume is calculated in the same way as volume, except that its length, width and height are measured from the inside.
extreme
Cuboids and cubes have a square paper with a length of 24 cm. If you cut a small square at each of its four corners, you can make a carton without a lid. Now, how long should the side of the small square be cut?
Analysis: 20 14 the volume of cuboids and cubes in the sixth grade Olympic math problem in primary school: according to the meaning of the problem, it can be assumed that the side length of the cut small square is x, and the volume of the cut carton is expressed by the volume formula, because the side length of the carton is certain, that is, 2x+(12-x)+(12-x). The volume of the paper box is 2×2x( 12-x)( 12-x), so we can know the side length of the cut small square by calculating the unknown in 2x = 12-x, and we can solve it in the form of columns.
Solution: As shown in the figure.
Let the side length of the cut small square be x cm,
The volume of the paper box is V=x(24-2x)(24-2x),
=2×2x( 12-x)( 12-x)，
Because 2x+(12-x)+(12-x) = 24,
So when 2x= 12-x, its product,
2x= 12-x，
3x= 12，
x=4，
That is, when x=4, the product is also the carton volume.
Answer: the side length of the cut small square should be 4 cm.
Comments: The key to solve this problem is to express the volume of this carton according to the cubic volume formula. In order to make 2x, 12-x and 12-x in the volume formula equal, 2x in the formula is equal to 12-x, so that the volume of the paper box can be solved.
Tisso
How do pupils distinguish between cuboids and cubes? A hexahedron surrounded by six rectangles (two opposite faces may also be squares) is called a cuboid.
The three sides of a cuboid that intersect at the vertex are called the three degrees of the cuboid. The three dimensions of a cuboid are called its length, width and height in elementary mathematics.
A cuboid has six faces, and the areas of the two opposite faces are equal. There are twelve sides (that is, the intersection of adjacent surfaces), four parallel sides are equal in length, and there are eight vertices (that is, the point where every three sides intersect). The three sides that intersect at the vertex are length, width and height.
Three cuboids with equal degrees are called cubes. In other words, a cuboid with equal length, width and height is called a cube.
Like a cuboid, a cube has six faces, eight vertices and twelve sides.
Different from a cuboid, the six faces of a cube are congruent squares, and the twelve sides of the cube are of equal length.
Cubes are special cuboids.