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:
volume of the wood in the box

Answer

To find the volume of wood in the closed wooden box, we can follow these steps:

### Step 1: Calculate the external volume 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 formula for the volume of a cuboid is:
\[ \text{Volume} = L \times W \times H \]

Substituting the values:
\[ \text{External Volume} = 27 \, \text{cm} \times 19 \, \text{cm} \times 11 \, \text{cm} \]
\[ \text{External Volume} = 27 \times 19 \times 11 = 5643 \, \text{cm}^3 \]

### Step 2: Calculate the internal dimensions of the box.
Since the thickness of the wood is 1.5 cm, we need to subtract twice the thickness from each dimension to find the internal dimensions.

- Internal Length = External Length - 2 × Thickness
\[ \text{Internal Length} = 27 \, \text{cm} - 2 \times 1.5 \, \text{cm} = 27 - 3 = 24 \, \text{cm} \]

- Internal Width = External Width - 2 × Thickness
\[ \text{Internal Width} = 19 \, \text{cm} - 2 \times 1.5 \, \text{cm} = 19 - 3 = 16 \, \text{cm} \]

- Internal Height = External Height - 2 × Thickness
\[ \text{Internal Height} = 11 \, \text{cm} - 2 \times 1.5 \, \text{cm} = 11 - 3 = 8 \, \text{cm} \]

### Step 3: Calculate the internal volume of the box.
Using the internal dimensions calculated:
\[ \text{Internal Volume} = \text{Internal Length} \times \text{Internal Width} \times \text{Internal Height} \]
\[ \text{Internal Volume} = 24 \, \text{cm} \times 16 \, \text{cm} \times 8 \, \text{cm} \]
\[ \text{Internal Volume} = 3072 \, \text{cm}^3 \]

### Step 4: Calculate the volume of the wood.
To find the volume of the wood, we subtract the internal volume from the external volume:
\[ \text{Volume of Wood} = \text{External Volume} - \text{Internal Volume} \]
\[ \text{Volume of Wood} = 5643 \, \text{cm}^3 - 3072 \, \text{cm}^3 \]
\[ \text{Volume of Wood} = 2571 \, \text{cm}^3 \]

### Final Answer:
The volume of the wood in the box is **2571 cm³**.

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