Six cubes, each with 12 cm edge, are joined end to end. Find the surface area of the resulting cuboid.

Answer

To find the surface area of the resulting cuboid formed by joining six cubes, each with a 12 cm edge, we can follow these steps:

### Step 1: Determine the dimensions of the cuboid
When six cubes are joined end to end, the dimensions of the resulting cuboid can be calculated as follows:

- **Length (L)**: Since each cube has an edge of 12 cm, the total length when six cubes are joined is:
\[ L = 6 \times 12 \text{ cm} = 72 \text{ cm} \]

- **Breadth (B)**: The breadth remains the same as the edge of the cube:
\[ B = 12 \text{ cm} \]

- **Height (H)**: The height also remains the same as the edge of the cube:
\[ H = 12 \text{ cm} \]

### Step 2: Use the formula for the surface area of a cuboid
The formula for the total surface area (SA) of a cuboid is given by:
\[ SA = 2(LB + LH + BH) \]
Substituting the values we found:
- \( L = 72 \text{ cm} \)
- \( B = 12 \text{ cm} \)
- \( H = 12 \text{ cm} \)

### Step 3: Calculate each term in the surface area formula
1. Calculate \( LB \):
\[ LB = 72 \times 12 = 864 \text{ cm}^2 \]

2. Calculate \( LH \):
\[ LH = 72 \times 12 = 864 \text{ cm}^2 \]

3. Calculate \( BH \):
\[ BH = 12 \times 12 = 144 \text{ cm}^2 \]

### Step 4: Substitute back into the surface area formula
Now, substitute these values back into the surface area formula:
\[ SA = 2(864 + 864 + 144) \]

### Step 5: Simplify the expression
1. First, add the terms inside the parentheses:
\[ 864 + 864 + 144 = 1872 \]

2. Now multiply by 2:
\[ SA = 2 \times 1872 = 3744 \text{ cm}^2 \]

### Conclusion
The surface area of the resulting cuboid is:
\[ \text{Surface Area} = 3744 \text{ cm}^2 \]

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