Two cubes of sides 6 cm each are kept side by side to form a rectangular parallelopiped. The area (in sq. cm) of the whole suface of the rectangular parallelopiped is

Options

A. 432
B. 360
C. 396
D. 340

Answer

To find the surface area of the rectangular parallelepiped formed by placing two cubes of side 6 cm side by side, we will follow these steps:

### Step 1: Understand the dimensions of the rectangular parallelepiped
When two cubes of side 6 cm are placed side by side, the dimensions of the rectangular parallelepiped will be:
- Length (l) = 2 × side of the cube = 2 × 6 cm = 12 cm
- Width (w) = side of the cube = 6 cm
- Height (h) = side of the cube = 6 cm

### Step 2: Use the formula for the surface area of a rectangular parallelepiped
The formula for the surface area (SA) of a rectangular parallelepiped is given by:
\[ SA = 2(lw + lh + wh) \]

### Step 3: Substitute the dimensions into the formula
Now, substituting the values we found:
- l = 12 cm
- w = 6 cm
- h = 6 cm

We calculate:
\[ SA = 2(12 \times 6 + 12 \times 6 + 6 \times 6) \]

### Step 4: Calculate each term
Calculating each term:
- \( lw = 12 \times 6 = 72 \)
- \( lh = 12 \times 6 = 72 \)
- \( wh = 6 \times 6 = 36 \)

### Step 5: Add the terms together
Now, add these values:
\[ SA = 2(72 + 72 + 36) = 2(180) \]

### Step 6: Final calculation
Now, multiply by 2:
\[ SA = 2 \times 180 = 360 \text{ sq. cm} \]

### Conclusion
The area of the whole surface of the rectangular parallelepiped is **360 sq. cm**.

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