A metallic sheet is a rectangular shape with dimensions 48 m `xx` 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of each square is 8 m, then the volume of the box is

Options

A. 4830 `m^3`
B. 5120` m^3`
C. 6420 `m^3`
D. 8960 `m^3`

Answer

To find the volume of the open box formed by cutting squares from the corners of a rectangular metallic sheet, we can follow these steps:

### Step 1: Understand the dimensions of the metallic sheet
The dimensions of the metallic sheet are given as:
- Length = 48 m
- Width = 36 m

### Step 2: Determine the size of the squares cut from each corner
Each square cut from the corners has a side length of:
- Side length of square = 8 m

### Step 3: Calculate the new dimensions of the box
After cutting off the squares, the new dimensions of the box can be calculated as follows:

#### Length of the box:
- Original length = 48 m
- Length reduced by the squares cut from both ends = 8 m + 8 m = 16 m
- New length = 48 m - 16 m = 32 m

#### Width of the box:
- Original width = 36 m
- Width reduced by the squares cut from both ends = 8 m + 8 m = 16 m
- New width = 36 m - 16 m = 20 m

### Step 4: Determine the height of the box
The height of the box is equal to the side length of the squares cut off:
- Height = 8 m

### Step 5: Calculate the volume of the box
The volume \( V \) of the box can be calculated using the formula:
\[ V = \text{Length} \times \text{Width} \times \text{Height} \]

Substituting the values we found:
\[ V = 32 \, \text{m} \times 20 \, \text{m} \times 8 \, \text{m} \]

### Step 6: Perform the multiplication
Calculating the volume:
1. First, calculate \( 32 \times 20 = 640 \)
2. Then, multiply by the height: \( 640 \times 8 = 5120 \)

Thus, the volume of the box is:
\[ V = 5120 \, \text{m}^3 \]

### Final Answer
The volume of the box is **5120 m³**.

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