Three cubes are kept adjacently, edge to edge. If the edge of each cube is 7 cm, find the total surface area of the resulting cuboid.

Answer

To find the total surface area of the resulting cuboid formed by three adjacent cubes, we can follow these steps:

### Step 1: Understand the dimensions of the cuboid
When three cubes with an edge length of 7 cm are placed edge to edge, they form a cuboid. The dimensions of the resulting cuboid will be:
- Length (L) = 3 times the edge of the cube = 3 × 7 cm = 21 cm
- Width (W) = edge of the cube = 7 cm
- Height (H) = edge of the cube = 7 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:
\[ SA = 2(LW + LH + WH) \]

### Step 3: Substitute the values into the formula
Now, substitute the values of L, W, and H into the formula:
- L = 21 cm
- W = 7 cm
- H = 7 cm

So,
\[ SA = 2(21 \times 7 + 21 \times 7 + 7 \times 7) \]

### Step 4: Calculate each term inside the brackets
Calculate each multiplication:
- \(21 \times 7 = 147\)
- \(21 \times 7 = 147\)
- \(7 \times 7 = 49\)

Now substitute these values back into the equation:
\[ SA = 2(147 + 147 + 49) \]

### Step 5: Add the values inside the brackets
Now, add the values:
\[ 147 + 147 + 49 = 343 \]

### Step 6: Multiply by 2
Now, multiply by 2:
\[ SA = 2 \times 343 = 686 \text{ cm}^2 \]

### Final Answer
The total surface area of the resulting cuboid is \(686 \text{ cm}^2\).

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