Three cubes each of side 5 cm are joined end to end. Find the surface area of the resulting cuboid.

Answer

To find the surface area of the resulting cuboid formed by joining three cubes of side 5 cm each, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the dimensions of the cubes:**
Each cube has a side length of 5 cm.

2. **Determine the dimensions of the resulting cuboid:**
- Since three cubes are joined end to end, the length of the cuboid will be the sum of the lengths of the three cubes.
- Length (L) = 5 cm + 5 cm + 5 cm = 15 cm
- The breadth (B) and height (H) of the cuboid will remain the same as the side of the cube.
- Breadth (B) = 5 cm
- Height (H) = 5 cm

3. **Use the formula for the surface area of a cuboid:**
The surface area (SA) of a cuboid is given by the formula:
\[ SA = 2(LB + BH + HL) \]
where L is the length, B is the breadth, and H is the height.

4. **Substitute the values into the formula:**
\[ SA = 2(15 \times 5 + 5 \times 5 + 5 \times 15) \]

5. **Calculate each term inside the parentheses:**
- \( LB = 15 \times 5 = 75 \)
- \( BH = 5 \times 5 = 25 \)
- \( HL = 5 \times 15 = 75 \)

6. **Add these values together:**
\[ 75 + 25 + 75 = 175 \]

7. **Multiply by 2 to find the total surface area:**
\[ SA = 2 \times 175 = 350 \text{ cm}^2 \]

### Final Answer:
The surface area of the resulting cuboid is **350 cm²**.

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