The external dimensions of a closed wooden box are 62 cm, 30 cm and 18 cm. If the box is made of 2-cm-tick wood, find the capacity of the box.

Answer

To find the capacity of the closed wooden box, we need to follow these steps:

### Step 1: Identify the external dimensions of the box.
The external dimensions are given as:
- Length (L) = 62 cm
- Breadth (B) = 30 cm
- Height (H) = 18 cm

### Step 2: Determine the thickness of the wood.
The thickness of the wood is given as 2 cm.

### Step 3: Calculate the internal dimensions of the box.
Since the wood is 2 cm thick on all sides, we need to subtract twice the thickness from each external dimension to find the internal dimensions.

- Internal Length = External Length - 2 * Thickness
\[ \text{Internal Length} = 62 \, \text{cm} - 2 \times 2 \, \text{cm} = 62 \, \text{cm} - 4 \, \text{cm} = 58 \, \text{cm} \]

- Internal Breadth = External Breadth - 2 * Thickness
\[ \text{Internal Breadth} = 30 \, \text{cm} - 2 \times 2 \, \text{cm} = 30 \, \text{cm} - 4 \, \text{cm} = 26 \, \text{cm} \]

- Internal Height = External Height - 2 * Thickness
\[ \text{Internal Height} = 18 \, \text{cm} - 2 \times 2 \, \text{cm} = 18 \, \text{cm} - 4 \, \text{cm} = 14 \, \text{cm} \]

### Step 4: Calculate the volume of the internal box.
The volume of the box (capacity) can be calculated using the formula:
\[ \text{Volume} = \text{Internal Length} \times \text{Internal Breadth} \times \text{Internal Height} \]
Substituting the internal dimensions:
\[ \text{Volume} = 58 \, \text{cm} \times 26 \, \text{cm} \times 14 \, \text{cm} \]

### Step 5: Perform the multiplication.
Calculating the volume step by step:
1. Calculate \(58 \times 26\):
\[ 58 \times 26 = 1508 \, \text{cm}^2 \]
2. Now multiply by the height:
\[ 1508 \, \text{cm}^2 \times 14 \, \text{cm} = 21012 \, \text{cm}^3 \]

### Final Answer:
The capacity of the box is \(21012 \, \text{cm}^3\).

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