79
Units of volume
Textbook: Part 3, lesson 79, pp. 34–36
GoalVolume is the number of unit cubes that fit inside a solid; mm³, cm³, dm³; 1 dm³ = 1 000 cm³; counting cubes layer by layer.
New words
volume · hajmcube · kubcubic centimetre · kub santimetr (sm³)cubic decimetre · kub detsimetr (dm³)
Explanation
The volume of a solid is the number of unit cubes that fit inside it. Unit cubes have edges 1 mm, 1 cm or 1 dm and volumes 1 mm³, 1 cm³, 1 dm³. We pack cubes into a cuboid layer by layer: volume = cubes in one layer × number of layers. The base of a cube with edge 1 dm holds 10 × 10 = 100 small cm³ cubes and it is 10 layers high, so 1 dm³ = 1 000 cm³. In the same way 1 cm³ = 1 000 mm³.
Worked examples
The bottom of a box holds 3 rows of 4 cubes: 12; 2 layers give 24 cubes. If each cube is 1 cm³, the volume is 24 cm³.
5 dm³ = 5 000 cm³; 7 cm³ = 7 000 mm³.
Class activity
“Cube building”: children build a cuboid from identical cubes and find its volume by counting the layers and the cubes in each layer.
Practice
1
1 dm³ = ? cm³
1000
2
9 dm³ = ? cm³
9000
3
3 cm³ = ? mm³
3000
4
In a box, 5 rows of 6 cubes of 1 cm³ were placed on the bottom, in 3 layers. What is the volume in cm³?
90
5
Planks are stacked in blocks: each block has 5 layers with 8 planks in each layer. How many planks are there in 6 blocks?
240