Three cubes each of side 15 cm are joined end to end. The total surface area of the cuboid is :

Options

A. 3150 `cm^(2)`
B. 1575 `cm^(2)`
C. 1012.5 `cm^(2)`
D. 576.4 `cm^(2)`

Answer

To find the total surface area of the cuboid formed by joining three cubes of side 15 cm each, we can follow these steps:

### Step 1: Determine the dimensions of the cuboid.
When three cubes of side 15 cm are joined end to end, the dimensions of the resulting cuboid will be:
- Length (L) = 15 cm + 15 cm + 15 cm = 45 cm
- Breadth (B) = 15 cm (same as the side of the cube)
- Height (H) = 15 cm (same as the side of the cube)

### Step 2: Use the formula for the total surface area of a cuboid.
The formula for the total surface area (TSA) of a cuboid is:
\[ \text{TSA} = 2(LB + BH + HL) \]

### Step 3: Substitute the values into the formula.
Substituting the values we found:
- L = 45 cm
- B = 15 cm
- H = 15 cm

Now, calculate each term:
1. \( LB = 45 \times 15 = 675 \, \text{cm}^2 \)
2. \( BH = 15 \times 15 = 225 \, \text{cm}^2 \)
3. \( HL = 15 \times 45 = 675 \, \text{cm}^2 \)

### Step 4: Calculate the total surface area.
Now substitute these values back into the TSA formula:
\[ \text{TSA} = 2(675 + 225 + 675) \]
\[ = 2(1575) \]
\[ = 3150 \, \text{cm}^2 \]

### Final Answer:
The total surface area of the cuboid is \( 3150 \, \text{cm}^2 \).

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