Two cubes with each side 10 cm are joined are joined end to end . Find the total surface area of the resulting cuboid.

Answer

To find the total surface area of the resulting cuboid formed by joining two cubes with each side measuring 10 cm, we can follow these steps:

### Step 1: Understand the dimensions of the cubes
Each cube has a side length of 10 cm. When two cubes are joined end to end, the dimensions of the resulting cuboid will change.

### Step 2: Determine the dimensions of the cuboid
- **Length (L)**: Since the two cubes are joined end to end, the total length of the cuboid will be the sum of the lengths of both cubes. Therefore,
\[ L = 10 \, \text{cm} + 10 \, \text{cm} = 20 \, \text{cm} \]
- **Breadth (B)**: The breadth of the cuboid remains the same as the side of the cube, which is
\[ B = 10 \, \text{cm} \]
- **Height (H)**: The height of the cuboid also remains the same as the side of the cube, which is
\[ H = 10 \, \text{cm} \]

### Step 3: Use the formula for the total surface area of a cuboid
The formula for the total surface area (TSA) of a cuboid is:
\[ \text{TSA} = 2 \times (L \times B + B \times H + L \times H) \]

### Step 4: Substitute the values into the formula
Now we will substitute the values of L, B, and H into the formula:
\[ \text{TSA} = 2 \times (20 \, \text{cm} \times 10 \, \text{cm} + 10 \, \text{cm} \times 10 \, \text{cm} + 20 \, \text{cm} \times 10 \, \text{cm}) \]

### Step 5: Calculate the individual areas
Calculating each term inside the parentheses:
- \(20 \, \text{cm} \times 10 \, \text{cm} = 200 \, \text{cm}^2\)
- \(10 \, \text{cm} \times 10 \, \text{cm} = 100 \, \text{cm}^2\)
- \(20 \, \text{cm} \times 10 \, \text{cm} = 200 \, \text{cm}^2\)

### Step 6: Sum the areas
Now, add these areas together:
\[ 200 \, \text{cm}^2 + 100 \, \text{cm}^2 + 200 \, \text{cm}^2 = 500 \, \text{cm}^2 \]

### Step 7: Multiply by 2 for the total surface area
Finally, multiply by 2 to find the total surface area:
\[ \text{TSA} = 2 \times 500 \, \text{cm}^2 = 1000 \, \text{cm}^2 \]

### Conclusion
The total surface area of the resulting cuboid is
\[ \boxed{1000 \, \text{cm}^2} \]