🧊 Volume with Cubes: Cuboids

How many cubes fit inside a box? We will stack cubes layer by layer to find the volume. Let’s begin!

A cube with every edge 1 centimetre long is called a unit cube. Its volume is 1 cubic centimetre. The volume of a box is the number of unit cubes that fit inside it.

Let’s fill the box layer by layer. The bottom layer has 4 columns and 3 rows: 4 × 3 = 12 cubes. The second layer has 12 more cubes. In all, 12 + 12 = 24 cubes. The volume of the box is 24 cubic centimetres.

The bottom layer is called the base. The number of cubes that fit on the base is the same as the base area: 4 × 3 = 12. The number of layers is the height: 2. So volume = base area × height. 12 × 2 = 24.

Another box: its base is 5 × 2, that is 10 cubes. There are three layers. Each layer has 10 cubes, so 10 × 3 = 30 cubic centimetres in all.

Very different boxes can have the same volume. 4 × 3 × 2 = 24, 6 × 4 × 1 = 24 and 2 × 2 × 6 = 24. One is wide and flat, one is narrow and tall, but all three are 24 cubic centimetres.

A cube with edges of 10 centimetres has a volume of 10 × 10 × 10 = 1000 cubic centimetres. This is called 1 cubic decimetre, and it holds exactly 1 litre of water. So 1 dm³ = 1 L, and 1 cm³ = 1 mL.

Let’s look at a structure made of cubes from different sides. From the front it looks like a staircase, from above we see 5 squares, and from the right we see towers of 2 and 3. This structure has 9 unit cubes.

In real life: a fish tank with a base of 5 decimetres × 3 decimetres and a height of 4 decimetres. The base area is 15, and the volume is 15 × 4 = 60 cubic decimetres. Since 1 dm³ = 1 L, the tank holds exactly 60 litres of water.

Summary: volume is the number of unit cubes that fit inside. Volume is base area times height. Boxes with different shapes can have the same volume. 1 cubic decimetre is 1 litre. Now try it in Cube Towers!