A wooden box measures 10 cm x 6 cm x 5 cm. Thickness of wood is 2 cm. Find the volume of the wood required to make the box

Answer

To find the volume of wood required to make the wooden box, we will first calculate the outer volume of the box and then the inner volume after accounting for the thickness of the wood. Finally, we will subtract the inner volume from the outer volume to find the volume of wood used.

### Step-by-Step Solution:

1. **Identify the outer dimensions of the box:**
- Length (L) = 10 cm
- Breadth (B) = 6 cm
- Height (H) = 5 cm

2. **Calculate the outer volume of the box:**
\[ \text{Outer Volume} = L \times B \times H = 10 \, \text{cm} \times 6 \, \text{cm} \times 5 \, \text{cm} \]
\[ \text{Outer Volume} = 300 \, \text{cm}^3 \]

3. **Determine the inner dimensions of the box:**
- The thickness of the wood is 2 cm. Therefore, we need to subtract twice the thickness from each dimension to find the inner dimensions.
- Inner Length = Outer Length - 2 × Thickness = \(10 \, \text{cm} - 2 \times 2 \, \text{cm} = 10 \, \text{cm} - 4 \, \text{cm} = 6 \, \text{cm}\)
- Inner Breadth = Outer Breadth - 2 × Thickness = \(6 \, \text{cm} - 2 \times 2 \, \text{cm} = 6 \, \text{cm} - 4 \, \text{cm} = 2 \, \text{cm}\)
- Inner Height = Outer Height - 2 × Thickness = \(5 \, \text{cm} - 2 \times 2 \, \text{cm} = 5 \, \text{cm} - 4 \, \text{cm} = 1 \, \text{cm}\)

4. **Calculate the inner volume of the box:**
\[ \text{Inner Volume} = \text{Inner Length} \times \text{Inner Breadth} \times \text{Inner Height} = 6 \, \text{cm} \times 2 \, \text{cm} \times 1 \, \text{cm} \]
\[ \text{Inner Volume} = 12 \, \text{cm}^3 \]

5. **Calculate the volume of wood required:**
\[ \text{Volume of Wood} = \text{Outer Volume} - \text{Inner Volume} = 300 \, \text{cm}^3 - 12 \, \text{cm}^3 \]
\[ \text{Volume of Wood} = 288 \, \text{cm}^3 \]

### Final Answer:
The volume of wood required to make the box is **288 cm³**.