The internal length , breadth and height of a closed box are 1 m , 80 cm and 25 cm respectively . If its sides are made of 2.5 cm thick wood , find
the capacity of the box
(ii) the volume of wood used to make the box.

Answer

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

### Step 1: Convert all dimensions to the same unit
The internal dimensions of the box are given as:
- Length = 1 m = 100 cm
- Breadth = 80 cm
- Height = 25 cm

### Step 2: Calculate the external dimensions
The thickness of the wood is given as 2.5 cm. To find the external dimensions, we add twice the thickness to each internal dimension (once for each side).

- External Length = Internal Length + 2 × Thickness
\[ = 100 \, \text{cm} + 2 \times 2.5 \, \text{cm} = 100 \, \text{cm} + 5 \, \text{cm} = 105 \, \text{cm} \]

- External Breadth = Internal Breadth + 2 × Thickness
\[ = 80 \, \text{cm} + 2 \times 2.5 \, \text{cm} = 80 \, \text{cm} + 5 \, \text{cm} = 85 \, \text{cm} \]

- External Height = Internal Height + 2 × Thickness
\[ = 25 \, \text{cm} + 2 \times 2.5 \, \text{cm} = 25 \, \text{cm} + 5 \, \text{cm} = 30 \, \text{cm} \]

### Step 3: Calculate the capacity of the box
The capacity of the box is given by the formula:
\[ \text{Capacity} = \text{Internal Length} \times \text{Internal Breadth} \times \text{Internal Height} \]
Substituting the internal dimensions:
\[ = 100 \, \text{cm} \times 80 \, \text{cm} \times 25 \, \text{cm} \]
Calculating this gives:
\[ = 100 \times 80 \times 25 = 200000 \, \text{cm}^3 \]

To convert this to cubic meters:
\[ \text{Capacity in m}^3 = \frac{200000}{1000000} = 0.2 \, \text{m}^3 \]

### Step 4: Calculate the volume of wood used
The volume of wood is calculated by subtracting the internal volume from the external volume.

- External Volume = External Length × External Breadth × External Height
\[ = 105 \, \text{cm} \times 85 \, \text{cm} \times 30 \, \text{cm} \]
Calculating this gives:
\[ = 105 \times 85 \times 30 = 267750 \, \text{cm}^3 \]

- Internal Volume (already calculated) = 200000 cm³

Now, we find the volume of wood:
\[ \text{Volume of wood} = \text{External Volume} - \text{Internal Volume} \]
\[ = 267750 \, \text{cm}^3 - 200000 \, \text{cm}^3 = 67750 \, \text{cm}^3 \]

To convert this to cubic meters:
\[ \text{Volume of wood in m}^3 = \frac{67750}{1000000} = 0.067775 \, \text{m}^3 \]

### Final Answers
(i) The capacity of the box is **0.2 m³**.
(ii) The volume of wood used to make the box is **0.067775 m³**.