Find the volume of wood used to make a closed box of outer dimensionis `60 cm xx 45 cm xx32cm`, the thickness of wook beign 2.5 cm all around.

Answer

To find the volume of wood used to make a closed box with given outer dimensions and thickness, we can follow these steps:

### Step 1: Identify the outer dimensions of the box.
The outer dimensions of the box are given as:
- Length (L) = 60 cm
- Breadth (B) = 45 cm
- Height (H) = 32 cm

### Step 2: Calculate the volume of the outer box.
The volume \( V_{outer} \) of the outer box can be calculated using the formula for the volume of a rectangular prism:
\[ V_{outer} = L \times B \times H \]
Substituting the values:
\[ V_{outer} = 60 \, \text{cm} \times 45 \, \text{cm} \times 32 \, \text{cm} = 86400 \, \text{cm}^3 \]

### Step 3: Determine the inner dimensions of the box.
Since the thickness of the wood is 2.5 cm all around, we need to subtract twice the thickness from each dimension to find the inner dimensions:
- Inner Length = \( 60 \, \text{cm} - 2.5 \, \text{cm} - 2.5 \, \text{cm} = 55 \, \text{cm} \)
- Inner Breadth = \( 45 \, \text{cm} - 2.5 \, \text{cm} - 2.5 \, \text{cm} = 40 \, \text{cm} \)
- Inner Height = \( 32 \, \text{cm} - 2.5 \, \text{cm} - 2.5 \, \text{cm} = 27 \, \text{cm} \)

### Step 4: Calculate the volume of the inner box.
The volume \( V_{inner} \) of the inner box can be calculated using the same volume formula:
\[ V_{inner} = \text{Inner Length} \times \text{Inner Breadth} \times \text{Inner Height} \]
Substituting the inner dimensions:
\[ V_{inner} = 55 \, \text{cm} \times 40 \, \text{cm} \times 27 \, \text{cm} = 59400 \, \text{cm}^3 \]

### Step 5: Calculate the volume of the wood used.
The volume of the wood used can be found by subtracting the volume of the inner box from the volume of the outer box:
\[ V_{wood} = V_{outer} - V_{inner} \]
Substituting the volumes:
\[ V_{wood} = 86400 \, \text{cm}^3 - 59400 \, \text{cm}^3 = 27000 \, \text{cm}^3 \]

### Final Answer:
The volume of wood used to make the closed box is **27000 cm³**.

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