Three cubes, each with 8cm edge, are joined end to end. Find the total surface area of the resulting cuboid

Answer

**Step-by-Step Solution:**

1. **Identify the dimensions of the cubes:**
Each cube has an edge length of 8 cm.

2. **Determine the dimensions of the resulting cuboid:**
Since three cubes are joined end to end, the total length of the cuboid will be:
\[ \text{Length} = 3 \times \text{edge length} = 3 \times 8 \, \text{cm} = 24 \, \text{cm} \]
The height and breadth of the cuboid will remain the same as that of the cube, which is:
\[ \text{Height} = 8 \, \text{cm}, \quad \text{Breadth} = 8 \, \text{cm} \]

3. **Use the formula for the surface area of a cuboid:**
The formula for the total surface area \( A \) of a cuboid is given by:
\[ A = 2 \times (l \times b + b \times h + h \times l) \]
where \( l \) is the length, \( b \) is the breadth, and \( h \) is the height.

4. **Substitute the values into the formula:**
Here, \( l = 24 \, \text{cm} \), \( b = 8 \, \text{cm} \), and \( h = 8 \, \text{cm} \). Substituting these values into the formula:
\[ A = 2 \times (24 \times 8 + 8 \times 8 + 8 \times 24) \]

5. **Calculate each term inside the parentheses:**
- \( 24 \times 8 = 192 \)
- \( 8 \times 8 = 64 \)
- \( 8 \times 24 = 192 \)

Now, add these values together:
\[ 192 + 64 + 192 = 448 \]

6. **Multiply by 2 to find the total surface area:**
\[ A = 2 \times 448 = 896 \, \text{cm}^2 \]

**Final Answer:**
The total surface area of the resulting cuboid is \( 896 \, \text{cm}^2 \).

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