Find the volume of wood used to make a closed rectangular box of outer dimensions `60 cm xx 45 cm xx 32 cm`, the thickness of wood being 2.5 cm all around. Also find the capacity of the box.

Answer

To find the volume of wood used to make a closed rectangular box and its capacity, 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 formula for the volume of a rectangular box is:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]
- Substituting the outer dimensions:
\[ \text{Volume of outer box} = 60 \, \text{cm} \times 45 \, \text{cm} \times 32 \, \text{cm} = 86,400 \, \text{cm}^3 \]

### 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 this thickness from each dimension:
- Inner Length = Outer Length - 2 × Thickness
\[ \text{Inner Length} = 60 \, \text{cm} - 2 \times 2.5 \, \text{cm} = 60 \, \text{cm} - 5 \, \text{cm} = 55 \, \text{cm} \]
- Inner Breadth = Outer Breadth - 2 × Thickness
\[ \text{Inner Breadth} = 45 \, \text{cm} - 2 \times 2.5 \, \text{cm} = 45 \, \text{cm} - 5 \, \text{cm} = 40 \, \text{cm} \]
- Inner Height = Outer Height - 2 × Thickness
\[ \text{Inner Height} = 32 \, \text{cm} - 2 \times 2.5 \, \text{cm} = 32 \, \text{cm} - 5 \, \text{cm} = 27 \, \text{cm} \]

### Step 4: Calculate the volume of the inner box.
- Using the inner dimensions, we can find the volume of the inner box:
\[ \text{Volume of inner box} = \text{Inner Length} \times \text{Inner Breadth} \times \text{Inner Height} \]
- Substituting the inner dimensions:
\[ \text{Volume of inner box} = 55 \, \text{cm} \times 40 \, \text{cm} \times 27 \, \text{cm} = 59,400 \, \text{cm}^3 \]

### Step 5: Calculate the volume of wood used.
- The volume of wood used is the difference between the volume of the outer box and the volume of the inner box:
\[ \text{Volume of wood} = \text{Volume of outer box} - \text{Volume of inner box} \]
- Substituting the calculated volumes:
\[ \text{Volume of wood} = 86,400 \, \text{cm}^3 - 59,400 \, \text{cm}^3 = 27,000 \, \text{cm}^3 \]

### Step 6: Find the capacity of the box.
- The capacity of the box is equal to the volume of the inner box:
\[ \text{Capacity of the box} = \text{Volume of inner box} = 59,400 \, \text{cm}^3 \]

### Final Answers:
- Volume of wood used: **27,000 cm³**
- Capacity of the box: **59,400 cm³**

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