The external dimension of an open box are `40 cm xx 30 cm xx 35 cm`. All of its walls are 2.5 cm thick, find (i) the capacity of the box, (ii) the wood used in the box.

Answer

To solve the problem step by step, we will find the capacity of the open box and the volume of wood used in its construction.

### Step 1: Determine the inner dimensions of the box
The external dimensions of the box are:
- Length (L) = 40 cm
- Breadth (B) = 30 cm
- Height (H) = 35 cm

The thickness of the walls is 2.5 cm. Since the box is open from the top, we will only subtract the thickness from the height once.

**Inner Length**:
\[ \text{Inner Length} = \text{External Length} - 2 \times \text{Thickness} = 40 \, \text{cm} - 2 \times 2.5 \, \text{cm} = 40 \, \text{cm} - 5 \, \text{cm} = 35 \, \text{cm} \]

**Inner Breadth**:
\[ \text{Inner Breadth} = \text{External Breadth} - 2 \times \text{Thickness} = 30 \, \text{cm} - 2 \times 2.5 \, \text{cm} = 30 \, \text{cm} - 5 \, \text{cm} = 25 \, \text{cm} \]

**Inner Height**:
\[ \text{Inner Height} = \text{External Height} - \text{Thickness} = 35 \, \text{cm} - 2.5 \, \text{cm} = 32.5 \, \text{cm} \]

### Step 2: Calculate the volume of the inner cuboid (capacity of the box)
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the inner dimensions:
\[ V = 35 \, \text{cm} \times 25 \, \text{cm} \times 32.5 \, \text{cm} \]
Calculating this:
\[ V = 35 \times 25 \times 32.5 = 28437.5 \, \text{cm}^3 \]

### Step 3: Calculate the volume of the outer cuboid
Now we calculate the volume of the outer cuboid using the external dimensions:
\[ V_{\text{outer}} = \text{External Length} \times \text{External Breadth} \times \text{External Height} \]
Substituting the external dimensions:
\[ V_{\text{outer}} = 40 \, \text{cm} \times 30 \, \text{cm} \times 35 \, \text{cm} \]
Calculating this:
\[ V_{\text{outer}} = 40 \times 30 \times 35 = 42000 \, \text{cm}^3 \]

### Step 4: Calculate the volume of wood used in the box
The volume of wood used is the difference between the outer volume and the inner volume:
\[ \text{Volume of wood} = V_{\text{outer}} - V_{\text{inner}} \]
Substituting the values:
\[ \text{Volume of wood} = 42000 \, \text{cm}^3 - 28437.5 \, \text{cm}^3 = 13562.5 \, \text{cm}^3 \]

### Final Answers:
(i) The capacity of the box is \( 28437.5 \, \text{cm}^3 \).
(ii) The volume of wood used in the box is \( 13562.5 \, \text{cm}^3 \).