Two cubes each with 14 cm edge are joined face to face, thus farming a cuboid. What is the surface area of the resulting cuboid ?

Options

A. `3528 cm^2`
B. `2352 cm^2`
C. `1960 cm^2`
D. `1568 cm^2`

Answer

To find the surface area of the resulting cuboid formed by joining two cubes with an edge length of 14 cm, we can follow these steps:

### Step 1: Understand the dimensions of the cuboid
When two cubes with an edge of 14 cm are joined face to face, the dimensions of the resulting cuboid will be:
- Length (L) = 14 cm (the edge of one cube)
- Breadth (B) = 14 cm (the edge of the other cube)
- Height (H) = 14 cm + 14 cm = 28 cm (the combined height of the two cubes)

### Step 2: Write down the formula for the surface area of a cuboid
The formula for the total surface area (SA) of a cuboid is given by:
\[ SA = 2(LB + BH + HL) \]

### Step 3: Substitute the dimensions into the formula
Now, substituting the values of L, B, and H into the formula:
- L = 14 cm
- B = 14 cm
- H = 28 cm

So, we have:
\[ SA = 2(14 \times 14 + 14 \times 28 + 28 \times 14) \]

### Step 4: Calculate each term inside the parentheses
1. Calculate \( LB \):
\[ LB = 14 \times 14 = 196 \, \text{cm}^2 \]

2. Calculate \( BH \):
\[ BH = 14 \times 28 = 392 \, \text{cm}^2 \]

3. Calculate \( HL \):
\[ HL = 28 \times 14 = 392 \, \text{cm}^2 \]

### Step 5: Add the results from Step 4
Now, add these values together:
\[ LB + BH + HL = 196 + 392 + 392 = 980 \, \text{cm}^2 \]

### Step 6: Multiply by 2 to find the total surface area
Finally, multiply the sum by 2:
\[ SA = 2 \times 980 = 1960 \, \text{cm}^2 \]

### Final Answer
The surface area of the resulting cuboid is **1960 cm²**.

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