The meaning of volume:
The space occupied by an object is called its volume.
Knowledge point 2
volume unit
Commonly used unit of volume: cubic centimeter, cubic decimeter and cubic meter. These three units are denoted by letters as cm3 and dm3 m3.
The volume of a fingertip is about 1 cm3, the volume of a chalk box is about 1 dm3, and the volume of a 29-inch TV box is about 1 m3.
Units of volume conversion: advanced units × low units.
Low-level unit and high-level unit
Propulsion rate: 1 m3 = 1000 cubic decimeter = 1000000 cubic centimeter.
1 cubic decimeter = 1000 cubic centimeter = 1 liter = 1000 ml.
1 cm3 = 1 ml
1 m3 = 1000 1dm 3 = 1000 1 m3 = 100 0000 cm3
1 square meter = 100 square decimeter = 10000 square centimeter 1 square kilometer = 100 hectare = 100000 square meter.
Weight unit rate, time unit rate and length unit rate
Tracking training
1. Fill in the appropriate unit of volume in the brackets of the following individuals.
(1) The volume of a refrigerator is about 185( )(2) The volume of a pile of coal is about 2500 ().
(3) The volume of an eraser is about 6( )(4) The volume of an ink cartridge is about 168 ().
Knowledge point three
Volume formula of cuboid
Volume of cuboid = length× width× height V=abh
Length = Volume ÷ Width ÷ Height a=V÷b÷h Width = Volume ÷ Length ÷ Height B = V ÷ A ÷ H.
Height = volume ÷ length ÷ width H = V ÷ A ÷ B.
Tracking exercise
1. A brick is 10 cm long, 6 cm wide and 3.5 cm high, with a volume of () cubic centimeters.
The cuboid is 36 cubic meters in volume, 6 meters in length, 3 meters in width and () meters in height.
3. A cube with a surface area of 24 square centimeters and a volume of ().
4. A cuboid whose length, width and height are 4 decimeters, 3 decimeters and 1 decimeter respectively consists of () individuals.
A cube whose product is 1 cubic decimeter.
5. The length of a cuboid is12cm and the height is 8cm. The sum of the areas on both sides of the shaded part is 200 cm 2. How many cubic centimeters is the volume of this cuboid?
Step 6 fill in the form
Knowledge point four
Volume formula of cube
Volume of cube = side length × side length × side length v = a× a× a.
The volume formula of a cube is generally abbreviated as V= a3.
For example, what is the volume of a cube with a side length of 8 cm?
Consolidation exercise
(1) The sum of the sides of a cube is 24 cm, and its surface area is () square cm; The volume is () cubic centimeters.
(2) A cube goldfish bowl with a side length of 4m. If you pour a full tank of water into another rectangular fish tank with a length of 8 decimeters and a width of 2.5 decimeters, how many meters can the water surface rise?
(3) When the side length of a cube is enlarged by 2 times, its volume is enlarged by () times.
(4) How many cubic decimeters of wood do you need to make 140 cubes with a length of 5 cm?
(5) A carton factory produces a cubic carton with a length of 40 cm. How many cubic centimeters is its volume? How many cubic decimeters?
Knowledge point five
Unified formula of cuboid and cube volume
Volume of cuboid or cube = bottom area × height is expressed by letters: V=Sh.
Example: A cuboid wood is 4.5 meters long and has a cross-sectional area of 0.08 square meters. What is the volume of this piece of wood?
Tracking exercise
1, there is a cuboid with a square bottom area and a height of 20 cm, and the side expansion is just square.
Find the volume of this cuboid.
2. Immerse an iron block with a volume of 80 cubic centimeters into a rectangular container with a bottom area of 20 square centimeters, and the water level is 10 centimeters. How high is the water level if the iron block is taken out?
The bottom area of truck compartment is 4.8 square meters. Transport a cuboid packing box with side lengths of 0.4m, 0.6m and 0.5m respectively. If you stack two floors, this truck can hold at most () boxes.
Consolidation exercise
fill (up) a vacancy
1. A rectangle is 6 cm long, 4 cm wide and 2 cm high. The sum of its sides is () cm, the maximum area of the six faces is () cm 2, the surface area is () cm 2, and the volume is () cm 3.
2. The length of the cube is 12 decimeter, and the volume is () cubic decimeter.
The cuboid has a volume of 30 cubic centimeters, a length of 5 centimeters, a height of 3 centimeters and a width of () centimeters.
The bottom area of a cuboid is 0.2 square meters, the height is 8 decimeters, and the volume is () cubic decimeters.
The volume of a cube with a surface area of 54 square centimeters is () cubic centimeters.
6. When the side length of a cube is reduced by 3 times, its volume is reduced by () times.
7. A rectangular frame is 8 cm long, 6 cm wide and 4 cm high. It takes () cm of iron wire to make this frame, that is to say, it needs a cuboid () with a plastic plate on its surface, and * * * needs () plastic plate, that is to say, () water needs to be filled in it, and () the box has () cubic meters.
.
Second, judgment (tick in brackets means correct, and x means wrong).
1. unit of volume is greater than area unit, and area unit is greater than length unit. ()
2. The volume of cubes and cuboids can be calculated by multiplying the bottom area by the height. ()
3. Two cuboids with the same surface area must have the same volume. ()
4. The cuboid volume is the cuboid volume. ()
5. If a cuboid can be sawed into four identical cubes, the area in front of the cuboid is four times that of the bottom. ()
Third, choose
1. When the side length of the cube is enlarged by 2 times, the volume is enlarged by () times.
A.2 B.4 C.6 D.8
2. A rectangular piece of wood, length 1.5 meters, width and thickness are 2 decimeters. Saw it into four sections, and the surface area will increase at least () square decimeter.
16 C.24 D.32
3. The length, width and height of the cuboid are enlarged by 2 times, and the volume is enlarged by () times.
A.2 B.4 C.6 D.8
4. Compared with cuboids and cubes with equal surface areas, ().
A.this cube is very big. This cuboid is very big. C. it is equal.
5. Forging the cubic blank into cuboids, cubes and cuboids ().
A. Equal volume and unequal surface area
B. the volume and surface area are not equal.
C. the surface area is equal and the volume is unequal.
6. A vegetable cellar can hold 6 cubic meters of Chinese cabbage, and the () of this vegetable cellar is 6 cubic meters.
A. Volume B. Volume C. Surface area
Verb (abbreviation of verb) Calculate the following volume (unit: decimeter).