6 cubes, each of edge 4 cm, are joined end to end. What is the total surface area of the resulting cuboid?

Options

A. `416 cm^2`
B. `496cm^2`
C. `576cm^2`
D. `208cm^2`

Answer

To find the total surface area of the resulting cuboid formed by joining 6 cubes of edge 4 cm end to end, we will follow these steps:

### Step 1: Determine the dimensions of the cuboid
Each cube has an edge length of 4 cm. When 6 cubes are joined end to end, the dimensions of the resulting cuboid will be:
- Length (L) = 6 * edge length = 6 * 4 cm = 24 cm
- Width (W) = edge length = 4 cm
- Height (H) = edge length = 4 cm

### Step 2: Use the formula for total surface area of a cuboid
The formula for the total surface area (SA) of a cuboid is:
\[ SA = 2(LW + LH + WH) \]

### Step 3: Substitute the dimensions into the formula
Now, we will substitute the values of L, W, and H into the formula:
- L = 24 cm
- W = 4 cm
- H = 4 cm

Substituting these values:
\[ SA = 2(24 \times 4 + 24 \times 4 + 4 \times 4) \]

### Step 4: Calculate the individual areas
Now, we calculate each term inside the parentheses:
1. \( 24 \times 4 = 96 \)
2. \( 24 \times 4 = 96 \)
3. \( 4 \times 4 = 16 \)

So, we can rewrite the equation:
\[ SA = 2(96 + 96 + 16) \]

### Step 5: Sum the areas
Now, we sum the areas:
\[ 96 + 96 + 16 = 208 \]

### Step 6: Multiply by 2
Now, we multiply by 2 to find the total surface area:
\[ SA = 2 \times 208 = 416 \text{ cm}^2 \]

### Final Answer
The total surface area of the resulting cuboid is **416 cm²**.

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