Layer by layer

About this video

How many sugar cubes fit in a box, without counting them one by one? This animation fills a box with centimetre cubes to find out. A cube 1 centimetre long, wide and high is one cubic centimetre, written 1 cm³, about the size of a sugar cube. In a box 4 cm long, 3 cm wide and 2 cm high, the bottom layer fills cube by cube: 3 rows of 4, which is 4 × 3 = 12 cubes, the same number as the area of the bottom, 12 cm². The box is 2 cm high, so 2 layers fit: 12 × 2 = 24 cubes, a volume of 24 cm³.

The same steps work for every box: length × width counts the cubes in one layer, and the height counts the layers, so volume = length × width × height. A box 5 by 4 by 3 is built layer by layer to 60 cm³. A cube 3 cm along each edge holds 3 × 3 × 3 = 27 small cubes, which is why 3³ is called "3 cubed". Last, a cube 10 cm along each edge stacks 10 layers of 100 cubes: 1,000 cm³. Filled with water it holds exactly 1 litre, so 1 cm³ is 1 millilitre. This video goes with the How Much a Box Holds lesson of Geometry Level 1 on Knaph.

Transcript

1. 0:00A box of sugar cubes. How many fit inside, without counting them one by one?
2. 0:07Take a cube one centimetre long, wide and high. That's one cubic centimetre.
3. 0:15Fill the bottom of a box, four by three. Three rows of four.
4. 0:24Twelve cubes. Four times three, the same as the area of the bottom, twelve square centimetres.
5. 0:31The box is two high, so two layers fit. Twelve times two is twenty-four cubic centimetres.
6. 0:41Every box works the same way. Volume is length times width times height. Five, four and three make sixty.
7. 0:57In a cube, all three are the same. Three times three times three is twenty-seven. Three cubed.
8. 1:07Now a cube ten centimetres each way. Ten times ten times ten is a thousand cubic centimetres.
9. 1:16Fill it with water, and it holds exactly one litre. So one cubic centimetre is one millilitre.
10. 1:23Volume counts cubes, layer by layer.