An open rectangular box has the external measures as 98 cm, 84 cm, 77 cm and the thickness of wood is 2 cm. Then the volume of the wood is ____

Options

A. 70000 cu. cm
B. 64865 cu. cm
C. 60000 cu. cm
D. 84904 cu. cm

Answer

To find the volume of the wood used in the open rectangular box, we will follow these steps:

### Step 1: Calculate the External Volume
The external dimensions of the box are given as:
- Length (L) = 98 cm
- Width (W) = 84 cm
- Height (H) = 77 cm

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

Substituting the external dimensions:
\[ \text{External Volume} = 98 \, \text{cm} \times 84 \, \text{cm} \times 77 \, \text{cm} \]

Calculating this:
\[ \text{External Volume} = 98 \times 84 \times 77 = 633864 \, \text{cm}^3 \]

### Step 2: Calculate the Internal Dimensions
The thickness of the wood is given as 2 cm. Since the thickness affects both sides of each dimension, we will subtract 4 cm (2 cm from each side) from each external dimension to find the internal dimensions.

- Internal Length = External Length - 2 × Thickness
\[ \text{Internal Length} = 98 \, \text{cm} - 2 \times 2 \, \text{cm} = 98 - 4 = 94 \, \text{cm} \]

- Internal Width = External Width - 2 × Thickness
\[ \text{Internal Width} = 84 \, \text{cm} - 2 \times 2 \, \text{cm} = 84 - 4 = 80 \, \text{cm} \]

- Internal Height = External Height - 2 × Thickness
\[ \text{Internal Height} = 77 \, \text{cm} - 2 \times 2 \, \text{cm} = 77 - 4 = 73 \, \text{cm} \]

### Step 3: Calculate the Internal Volume
Now, we will calculate the internal volume using the internal dimensions:
\[ \text{Internal Volume} = \text{Internal Length} \times \text{Internal Width} \times \text{Internal Height} \]
\[ \text{Internal Volume} = 94 \, \text{cm} \times 80 \, \text{cm} \times 73 \, \text{cm} \]

Calculating this:
\[ \text{Internal Volume} = 94 \times 80 \times 73 = 548960 \, \text{cm}^3 \]

### Step 4: Calculate the Volume of the Wood
The volume of the wood is the difference between the external volume and the internal volume:
\[ \text{Volume of Wood} = \text{External Volume} - \text{Internal Volume} \]
\[ \text{Volume of Wood} = 633864 \, \text{cm}^3 - 548960 \, \text{cm}^3 \]
\[ \text{Volume of Wood} = 84904 \, \text{cm}^3 \]

### Final Answer
The volume of the wood is **84904 cm³**.

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