The external dimensions of a closed wooden box are 27cm, 19cm and 11cm. If the thickness of the wood in the box is 1.5 cm, find:
number of 4cm cubes that could be placed into the box.

Answer

To solve the problem step by step, we need to determine the internal dimensions of the wooden box and then calculate the volume of the box and the volume of the cubes. Finally, we will find out how many cubes can fit inside the box.

### Step 1: Determine the Internal Dimensions of the Box
The external dimensions of the box are given as:
- Length (L) = 27 cm
- Width (W) = 19 cm
- Height (H) = 11 cm

The thickness of the wood is 1.5 cm. To find the internal dimensions, we need to subtract twice the thickness from each external dimension (once for each side).

**Internal Length (IL)**:
\[ IL = L - 2 \times \text{thickness} = 27 \, \text{cm} - 2 \times 1.5 \, \text{cm} = 27 - 3 = 24 \, \text{cm} \]

**Internal Width (IW)**:
\[ IW = W - 2 \times \text{thickness} = 19 \, \text{cm} - 2 \times 1.5 \, \text{cm} = 19 - 3 = 16 \, \text{cm} \]

**Internal Height (IH)**:
\[ IH = H - 2 \times \text{thickness} = 11 \, \text{cm} - 2 \times 1.5 \, \text{cm} = 11 - 3 = 8 \, \text{cm} \]

### Step 2: Calculate the Internal Volume of the Box
Now, we can calculate the internal volume of the box using the internal dimensions:
\[ \text{Volume of the box} = IL \times IW \times IH \]
\[ \text{Volume} = 24 \, \text{cm} \times 16 \, \text{cm} \times 8 \, \text{cm} \]
\[ \text{Volume} = 3072 \, \text{cm}^3 \]

### Step 3: Calculate the Volume of a 4 cm Cube
Next, we calculate the volume of one cube with a side length of 4 cm:
\[ \text{Volume of one cube} = \text{side}^3 = 4 \, \text{cm} \times 4 \, \text{cm} \times 4 \, \text{cm} \]
\[ \text{Volume of one cube} = 64 \, \text{cm}^3 \]

### Step 4: Calculate the Number of Cubes that Fit in the Box
To find the number of cubes that can fit inside the box, we divide the internal volume of the box by the volume of one cube:
\[ \text{Number of cubes} = \frac{\text{Volume of the box}}{\text{Volume of one cube}} \]
\[ \text{Number of cubes} = \frac{3072 \, \text{cm}^3}{64 \, \text{cm}^3} \]
\[ \text{Number of cubes} = 48 \]

### Final Answer
The number of 4 cm cubes that could be placed into the box is **48**.