A box with a lid is made of wood which is 3 cm thick. Its external length, bredth and height are 56 cm, 39 cm and 30 cm respectivley. Find the capacity of the box. Also find the volume of wood used to make the box.

Answer

To solve the problem step by step, we will first calculate the external volume of the box, then find the internal dimensions, calculate the internal volume, and finally determine the volume of the wood used to make the box.

### Step 1: Calculate the External Volume of the Box
The external dimensions of the box are given as:
- Length (L) = 56 cm
- Breadth (B) = 39 cm
- Height (H) = 30 cm

The formula for the volume of a rectangular box is:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]

Substituting the values:
\[ \text{External Volume} = 56 \, \text{cm} \times 39 \, \text{cm} \times 30 \, \text{cm} \]

Calculating:
\[ \text{External Volume} = 56 \times 39 \times 30 = 65,520 \, \text{cm}^3 \]

### Step 2: Calculate the Internal Dimensions of the Box
The thickness of the wood is 3 cm. Therefore, we need to subtract twice the thickness from each external dimension to find the internal dimensions.

1. **Internal Length (L')**:
\[ L' = L - 2 \times \text{thickness} = 56 \, \text{cm} - 2 \times 3 \, \text{cm} = 56 - 6 = 50 \, \text{cm} \]

2. **Internal Breadth (B')**:
\[ B' = B - 2 \times \text{thickness} = 39 \, \text{cm} - 2 \times 3 \, \text{cm} = 39 - 6 = 33 \, \text{cm} \]

3. **Internal Height (H')**:
\[ H' = H - 2 \times \text{thickness} = 30 \, \text{cm} - 2 \times 3 \, \text{cm} = 30 - 6 = 24 \, \text{cm} \]

### Step 3: Calculate the Internal Volume of the Box
Now we can calculate the internal volume using the internal dimensions:
\[ \text{Internal Volume} = L' \times B' \times H' \]

Substituting the internal dimensions:
\[ \text{Internal Volume} = 50 \, \text{cm} \times 33 \, \text{cm} \times 24 \, \text{cm} \]

Calculating:
\[ \text{Internal Volume} = 50 \times 33 \times 24 = 39,600 \, \text{cm}^3 \]

### Step 4: Calculate the Volume of the Wood Used
The volume of the wood used to make the box can be found by subtracting the internal volume from the external volume:
\[ \text{Volume of Wood} = \text{External Volume} - \text{Internal Volume} \]

Substituting the values:
\[ \text{Volume of Wood} = 65,520 \, \text{cm}^3 - 39,600 \, \text{cm}^3 \]

Calculating:
\[ \text{Volume of Wood} = 25,920 \, \text{cm}^3 \]

### Final Answers
- **Capacity of the box (Internal Volume)**: 39,600 cm³
- **Volume of wood used**: 25,920 cm³