A cupboard made up of wood has the inner measures as 120 cm, 70 cm and 45 cm. If the thickness of the wood is 2.5 cm, then find the volume of the wood.

Options

A. `90750 cm^(3)`
B. `82125 cm^(3)`
C. `47000 cm^(3)`
D. `85000 cm^(3)`

Answer

To find the volume of wood used in the cupboard, we will follow these steps:

### Step 1: Calculate the inner volume of the cupboard.
The inner dimensions of the cupboard are given as:
- Length (L) = 120 cm
- Breadth (B) = 70 cm
- Height (H) = 45 cm

The formula for the volume of a cuboid is:
\[ \text{Volume} = L \times B \times H \]

Substituting the values:
\[ \text{Inner Volume} = 120 \, \text{cm} \times 70 \, \text{cm} \times 45 \, \text{cm} \]

Calculating:
\[ \text{Inner Volume} = 120 \times 70 \times 45 = 378000 \, \text{cm}^3 \]

### Step 2: Calculate the outer dimensions of the cupboard.
Given the thickness of the wood is 2.5 cm, we need to add this thickness to each dimension twice (once for each side).

- Outer Length = Inner Length + 2 × Thickness
\[ \text{Outer Length} = 120 \, \text{cm} + 2 \times 2.5 \, \text{cm} = 120 + 5 = 125 \, \text{cm} \]

- Outer Breadth = Inner Breadth + 2 × Thickness
\[ \text{Outer Breadth} = 70 \, \text{cm} + 2 \times 2.5 \, \text{cm} = 70 + 5 = 75 \, \text{cm} \]

- Outer Height = Inner Height + 2 × Thickness
\[ \text{Outer Height} = 45 \, \text{cm} + 2 \times 2.5 \, \text{cm} = 45 + 5 = 50 \, \text{cm} \]

### Step 3: Calculate the outer volume of the cupboard.
Using the outer dimensions calculated:
\[ \text{Outer Volume} = \text{Outer Length} \times \text{Outer Breadth} \times \text{Outer Height} \]
\[ \text{Outer Volume} = 125 \, \text{cm} \times 75 \, \text{cm} \times 50 \, \text{cm} \]

Calculating:
\[ \text{Outer Volume} = 125 \times 75 \times 50 = 468750 \, \text{cm}^3 \]

### Step 4: Calculate the volume of the wood.
The volume of wood used in the cupboard can be found by subtracting the inner volume from the outer volume:
\[ \text{Volume of Wood} = \text{Outer Volume} - \text{Inner Volume} \]
\[ \text{Volume of Wood} = 468750 \, \text{cm}^3 - 378000 \, \text{cm}^3 \]

Calculating:
\[ \text{Volume of Wood} = 90750 \, \text{cm}^3 \]

### Final Answer:
The volume of the wood used in the cupboard is \( 90750 \, \text{cm}^3 \).

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