Two identical cubes each of volume `64 cm^3` are joined together end to end. What is the surface area of the resulting cuboid?

Answer

To find the surface area of the resulting cuboid formed by joining two identical cubes, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Volume of One Cube**:
- Given that the volume of each cube is \(64 \, \text{cm}^3\).

2. **Find the Edge Length of the Cube**:
- The volume \(V\) of a cube is given by the formula:
\[ V = a^3 \]
where \(a\) is the edge length of the cube.
- Setting the volume equal to \(64 \, \text{cm}^3\):
\[ a^3 = 64 \]
- To find \(a\), take the cube root of both sides:
\[ a = \sqrt[3]{64} = 4 \, \text{cm} \]

3. **Determine the Dimensions of the Resulting Cuboid**:
- When two cubes are joined end to end, the length of the cuboid becomes \(2a\) and the breadth and height remain \(a\).
- Therefore:
- Length \(L = 2a = 2 \times 4 = 8 \, \text{cm}\)
- Breadth \(B = a = 4 \, \text{cm}\)
- Height \(H = a = 4 \, \text{cm}\)

4. **Calculate the Surface Area of the Cuboid**:
- The formula for the total surface area \(S\) of a cuboid is:
\[ S = 2(LB + BH + HL) \]
- Substituting the values of \(L\), \(B\), and \(H\):
\[ S = 2(8 \times 4 + 4 \times 4 + 4 \times 8) \]
- Calculate each term:
- \(LB = 8 \times 4 = 32\)
- \(BH = 4 \times 4 = 16\)
- \(HL = 4 \times 8 = 32\)
- Now sum these values:
\[ S = 2(32 + 16 + 32) = 2(80) = 160 \, \text{cm}^2 \]

### Final Answer:
The total surface area of the resulting cuboid is \(160 \, \text{cm}^2\).

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