Cubes, Volumes And... Sides

This activity is aimed at teaching the basics of solid geometry.

Kids are asked to build cubes of different volumes: half a litre, one litre, two litres and three litres, therefore 500 cm³, 1,000 cm³, 2,000 cm³ and 3,000 cm³, respectively.

Afterwards, we are asked to investigate on the respective sides of these cubes. Easy to compute in the case of the cube with capacity one litre, which by definition is 10 cm.

Regarding the other sides, we would like teach that the cube with a capacity of two litres doesn't have a side of 20 cm (as one might mistakenly venture) but ³√2,000 cm³ ≈ 12.56 cm.

Therefore, the doubling of volume capacity generates an increase in the side by a factor of 1.256.

Supplies

For this project, I've gathered up the following things:

• 12 straws per cube (one on each side). In total: 48, better if coloured differently
• Hot glue
• To prevent damage to the desk, parchment paper or other material (it is not required for the project, only to avoid damaging).

Step 1: How Long Are the Straws?

The first step is cutting the straws to the right length.

The idea is to build four cubes whose volume is half a litre, one litre, two litres and three litres respectively.

Therefore, knowing the volumes, the corresponding sides will be its cubic root.

+-----------+----------+
|  Volume   |   Side   |
+-----------+----------+
|   500 cm³ |  7,94 cm |
+-----------+----------+
| 1,000 cm³ | 10,00 cm |
+-----------+----------+
| 2,000 cm³ | 12,56 cm |
+-----------+----------+
| 3,000 cm³ | 14,42 cm |
+-----------+----------+

Step 2: Cube Construction

To make a cube, at least two people are needed: one to put the straws in place; another to glue them.

In the first picture, the unglued cube is shown, so that you can get an idea about the desired result. After the steps followed by my pupils.

Step 3: Reiterate for Each Cube

Of course, the cube construction procedure has to be repeated for each cube of every size.

Step 4: What Will Appear?

Above the four cubes of half litre, one litre, two litres and three litres. It is evident that the sides don't double when the volume doubles.

This is a surprisingly simple method for explaining a complex concept: the relationship between the side and volume ratio in a geometrical solid.

I have chosen the cube because it has the simplest calculations.

Step 5: Matryoshka Effect

The temptation to insert one cube inside the other and create a spectacular Matryoshka effect is simply irresistible!