② There are eleven kinds of development diagrams of cubes

③ Square coloring B: All the surfaces of a cube are painted with colors, and then cut into small cubes with edge length of 1. (cuboid is the same as)

There are 8 colors on three sides, and at the vertex

There are two colors on two sides: there are (edge length-2 × 12) to actually find the edge length of the cube after subtracting 2 from the edge length

There are colors on one side: there are (edge length-2 × 6) to actually find the surface area of the cube after subtracting 2 from the edge length <

④ The edge length of the cube is doubled, the surface area is quadrupled, and the area is tripled. The edge length of the cube has been expanded to twice the original volume, and the volume has been expanded to eight times, which has increased by seven times. The volume of a cube is three times that of the original cube.

⑤ if the edge length of a cube is a, then its edge length =12a. Surface area s: s = 6× a× a = 6a2 volume V= a×a×a= a3

⑥ unit of volume has: cubic meter, cubic decimeter, cubic centimeter 1 cubic decimeter =1 cubic centimeter 1 cubic meter =1 cubic decimeter

Volume units are: cubic meter, liter, ML 1 liter =1 cubic decimeter 1 mL =1 cubic centimeter 1 liter =1 mL

II. Cuboid

① A cuboid has six faces, 12 edges and 8 vertices, and at most three faces can be seen, and at least one face can be seen. A cuboid does not include cubes, but at most two faces are squares, at most four faces, and at most eight edges are equal.

② The surface development diagrams of cuboids with unequal length, width and height: 27 kinds in 141; 18 kinds of 231 styles; 6 kinds in 222; There are 3 kinds in triplicate and 54 kinds in * * *.

③ Number of faces of the object: two faces: first step (one in front and one on top)

Four faces: matchbox shell, leakage pipe, ventilation pipe, column, biscuit box

Five faces: fish tank, swimming pool, drawer, matchbox inner box, painting classroom wall (with a top face,

④ Surface area of a cuboid = (length× width+length× height+width× height )× 2 lateral area of a cuboid = perimeter of bottom surface× perimeter of high bottom surface = (length+width )× 2

⑤ One or several objects are superimposed on another object: surface area of these objects = surface area of the lower object+lateral area of all the upper objects

cuboid volume.

perimeter of bottom surface = lateral area height of cuboid

III. Calculation related to immersion of objects in water (which will appear in the competition)

① Heavy objects are completely immersed in water: volume of objects = volume of water surface rising = bottom area of container × height of water surface rising;

the rising height of the water surface = the volume of the object ÷ the bottom area of the container

② The heavy object is partially immersed in the water: the current height of the water surface = the volume of water ÷ (the bottom area of the container-the bottom area of the heavy object)

IV. Binding articles

① Two surfaces (usually upper and lower) are bound together in a cross, and the rope length = the circumference of two crosses+. Rope length = sum of cuboid edges+joint length =4 length +4 width +4 height+joint length

5. Trademark area around biscuit box = (bottom perimeter+joint length) × floor area of tall objects, i.e. occupied space

carpet or floor tile area of stairs = (height of each staircase+width of each staircase) ×