Six cubes, each of edge 2 cm, are joined end to end. What is the total surface area of the resulting cuboid in `cm^(2)` ?

Options

A. 96
B. 144
C. 104
D. 128

Answer

To find the total surface area of the resulting cuboid formed by joining six cubes, each with an edge of 2 cm, we can follow these steps:

### Step 1: Determine the dimensions of the cuboid
- Each cube has an edge length of 2 cm.
- When six cubes are joined end to end, the length of the cuboid will be the sum of the lengths of all six cubes.
- Therefore, the length \( L \) of the cuboid is:
\[ L = 6 \times 2 \text{ cm} = 12 \text{ cm} \]
- The breadth \( B \) and height \( H \) of the cuboid will be equal to the edge length of the cube, which is:
\[ B = H = 2 \text{ cm} \]

### Step 2: Use the formula for the total surface area of a cuboid
The formula for the total surface area \( A \) of a cuboid is given by:
\[ A = 2(LB + BH + HL) \]

### Step 3: Substitute the values into the formula
Now we can substitute the values of \( L \), \( B \), and \( H \) into the formula:
- \( L = 12 \text{ cm} \)
- \( B = 2 \text{ cm} \)
- \( H = 2 \text{ cm} \)

Substituting these values:
\[ A = 2(12 \times 2 + 2 \times 2 + 2 \times 12) \]

### Step 4: Calculate the individual areas
Now calculate each term inside the parentheses:
- \( LB = 12 \times 2 = 24 \)
- \( BH = 2 \times 2 = 4 \)
- \( HL = 2 \times 12 = 24 \)

Adding these together:
\[ 24 + 4 + 24 = 52 \]

### Step 5: Multiply by 2 to find the total surface area
Now, multiply by 2:
\[ A = 2 \times 52 = 104 \text{ cm}^2 \]

### Final Answer
The total surface area of the resulting cuboid is:
\[ \boxed{104 \text{ cm}^2} \]