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 each of side 12 cm end to end, we can follow these steps:

### Step 1: Determine the dimensions of the cuboid
When six cubes of side 12 cm are joined end to end, the dimensions of the resulting cuboid will be:
- Length (L) = Number of cubes × Side of each cube = 6 × 12 cm = 72 cm
- Breadth (B) = Side of the cube = 12 cm
- Height (H) = Side of the cube = 12 cm

### Step 2: Write the formula for the surface area of a cuboid
The formula for the surface area (SA) of a cuboid is given by:
\[ SA = 2(lb + bh + hl) \]
where:
- \( l \) = length
- \( b \) = breadth
- \( h \) = height

### Step 3: Substitute the values into the formula
Substituting the values we found:
- Length (L) = 72 cm
- Breadth (B) = 12 cm
- Height (H) = 12 cm

The surface area can be calculated as:
\[ SA = 2(72 \times 12 + 12 \times 12 + 12 \times 72) \]

### Step 4: Calculate each term inside the brackets
1. Calculate \( 72 \times 12 \):
\[ 72 \times 12 = 864 \]
2. Calculate \( 12 \times 12 \):
\[ 12 \times 12 = 144 \]
3. Calculate \( 12 \times 72 \):
\[ 12 \times 72 = 864 \]

### Step 5: Sum the terms inside the brackets
Now, we can add these results together:
\[ 864 + 144 + 864 = 1872 \]

### Step 6: Multiply by 2 to find the surface area
Now, multiply by 2 to find the total surface area:
\[ SA = 2 \times 1872 = 3744 \text{ cm}^2 \]

### Final Answer
The surface area of the cuboid formed by joining six cubes of side 12 cm each is:
\[ \text{Surface Area} = 3744 \text{ cm}^2 \]

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