Find the volume of wood required to make a closed box of external dimensions , 80 cm 75 cm and 60 cm the thickness of walls of the box being 2 cm throughout.

Answer

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

### Step 1: Identify the External Dimensions
The external dimensions of the box are given as:
- Length (L) = 80 cm
- Breadth (B) = 75 cm
- Height (H) = 60 cm

### Step 2: Calculate the Internal Dimensions
Since the thickness of the walls is 2 cm throughout, we need to subtract twice the thickness from each external dimension to find the internal dimensions.

- Internal Length = External Length - 2 * Thickness
\[ \text{Internal Length} = 80 \, \text{cm} - 2 \times 2 \, \text{cm} = 80 \, \text{cm} - 4 \, \text{cm} = 76 \, \text{cm} \]

- Internal Breadth = External Breadth - 2 * Thickness
\[ \text{Internal Breadth} = 75 \, \text{cm} - 2 \times 2 \, \text{cm} = 75 \, \text{cm} - 4 \, \text{cm} = 71 \, \text{cm} \]

- Internal Height = External Height - 2 * Thickness
\[ \text{Internal Height} = 60 \, \text{cm} - 2 \times 2 \, \text{cm} = 60 \, \text{cm} - 4 \, \text{cm} = 56 \, \text{cm} \]

### Step 3: Calculate the Volume of the External Box
The volume of the external box can be calculated using the formula for the volume of a rectangular prism:
\[ \text{Volume}_{\text{external}} = L \times B \times H \]
Substituting the external dimensions:
\[ \text{Volume}_{\text{external}} = 80 \, \text{cm} \times 75 \, \text{cm} \times 60 \, \text{cm} \]
Calculating this gives:
\[ \text{Volume}_{\text{external}} = 360000 \, \text{cm}^3 \]

### Step 4: Calculate the Volume of the Internal Box
Using the internal dimensions:
\[ \text{Volume}_{\text{internal}} = \text{Internal Length} \times \text{Internal Breadth} \times \text{Internal Height} \]
Substituting the internal dimensions:
\[ \text{Volume}_{\text{internal}} = 76 \, \text{cm} \times 71 \, \text{cm} \times 56 \, \text{cm} \]
Calculating this gives:
\[ \text{Volume}_{\text{internal}} = 302176 \, \text{cm}^3 \]

### Step 5: Calculate the Volume of Wood Required
The volume of wood required is the difference between the external volume and the internal volume:
\[ \text{Volume}_{\text{wood}} = \text{Volume}_{\text{external}} - \text{Volume}_{\text{internal}} \]
Substituting the values:
\[ \text{Volume}_{\text{wood}} = 360000 \, \text{cm}^3 - 302176 \, \text{cm}^3 \]
Calculating this gives:
\[ \text{Volume}_{\text{wood}} = 57824 \, \text{cm}^3 \]

### Final Answer
The volume of wood required to make the closed box is **57824 cm³**.

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