Find the volume of wood required for a closed wooden box with external dimensions `15cm xx 12cmxx8cm`, if the wood is 0.5 cm thick.

Answer

To find the volume of wood required for a closed wooden box with external dimensions of 15 cm x 12 cm x 8 cm and a thickness of 0.5 cm, we can follow these steps:

### Step 1: Identify External Dimensions
The external dimensions of the box are given as:
- Length (L) = 15 cm
- Breadth (B) = 12 cm
- Height (H) = 8 cm

### Step 2: Calculate Internal Dimensions
Since the wood is 0.5 cm thick, we need to subtract twice the thickness from each dimension to find the internal dimensions.

- Internal Length = External Length - 2 × Thickness
\[ \text{Internal Length} = 15 \, \text{cm} - 2 \times 0.5 \, \text{cm} = 15 \, \text{cm} - 1 \, \text{cm} = 14 \, \text{cm} \]

- Internal Breadth = External Breadth - 2 × Thickness
\[ \text{Internal Breadth} = 12 \, \text{cm} - 2 \times 0.5 \, \text{cm} = 12 \, \text{cm} - 1 \, \text{cm} = 11 \, \text{cm} \]

- Internal Height = External Height - 2 × Thickness
\[ \text{Internal Height} = 8 \, \text{cm} - 2 \times 0.5 \, \text{cm} = 8 \, \text{cm} - 1 \, \text{cm} = 7 \, \text{cm} \]

### Step 3: Calculate Internal Volume
Now, we can calculate the volume of the internal cuboid using the formula:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the internal dimensions:
\[ \text{Internal Volume} = 14 \, \text{cm} \times 11 \, \text{cm} \times 7 \, \text{cm} \]
Calculating this step-by-step:
- First, calculate \(14 \times 11 = 154 \, \text{cm}^2\)
- Then, \(154 \times 7 = 1078 \, \text{cm}^3\)

### Step 4: Calculate External Volume
Next, we calculate the volume of the external cuboid using the external dimensions:
\[ \text{External Volume} = 15 \, \text{cm} \times 12 \, \text{cm} \times 8 \, \text{cm} \]
Calculating this step-by-step:
- First, calculate \(15 \times 12 = 180 \, \text{cm}^2\)
- Then, \(180 \times 8 = 1440 \, \text{cm}^3\)

### Step 5: Calculate Volume of Wood
Finally, to find the volume of wood required, we subtract the internal volume from the external volume:
\[ \text{Volume of Wood} = \text{External Volume} - \text{Internal Volume} \]
Substituting the values:
\[ \text{Volume of Wood} = 1440 \, \text{cm}^3 - 1078 \, \text{cm}^3 = 362 \, \text{cm}^3 \]

### Final Answer
The volume of wood required for the box is **362 cm³**.

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