Six cubes each of side 12 cm are joined end to end .Find the surface area of the cuboid so formed .

Answer

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

### Step-by-Step Solution:

1. **Understand the Problem**: We have six cubes, each with a side length of 12 cm, joined end to end to form a cuboid.

2. **Determine the Dimensions of the Cuboid**:
- **Length (L)**: Since the cubes are joined end to end, the total length of the cuboid is the sum of the lengths of all six cubes.
\[ L = 6 \times \text{side of one cube} = 6 \times 12 \, \text{cm} = 72 \, \text{cm} \]
- **Breadth (B)**: The breadth of the cuboid is equal to the side of one cube.
\[ B = \text{side of one cube} = 12 \, \text{cm} \]
- **Height (H)**: The height of the cuboid is also equal to the side of one cube.
\[ H = \text{side of one cube} = 12 \, \text{cm} \]

3. **Use the Surface Area Formula for a Cuboid**:
The formula for the surface area (SA) of a cuboid is:
\[ SA = 2(LB + BH + HL) \]
Substituting the values we found:
\[ SA = 2(72 \times 12 + 12 \times 12 + 12 \times 72) \]

4. **Calculate Each Term**:
- Calculate \(LB\):
\[ LB = 72 \times 12 = 864 \]
- Calculate \(BH\):
\[ BH = 12 \times 12 = 144 \]
- Calculate \(HL\):
\[ HL = 12 \times 72 = 864 \]

5. **Combine the Terms**:
Now, substitute these values back into the surface area formula:
\[ SA = 2(864 + 144 + 864) \]
\[ SA = 2(1872) \]

6. **Final Calculation**:
\[ SA = 3744 \, \text{cm}^2 \]

### Final Answer:
The surface area of the cuboid formed is **3744 cm²**.