A cuboid is formed of 3 edges measuring 3,4 and 5 cm. It is sliced into two identical solids by a plane through a diagonal of the smallest of the faces. The surface area of the sliced section is

Options

A. `12" cm"^(2)`
B. `15" cm"^(2)`
C. `20" cm"^(2)`
D. `25" cm"^(2)`

Answer

To solve the problem, we need to find the surface area of the sliced section of a cuboid with dimensions 3 cm, 4 cm, and 5 cm. Let's go through the steps to find the solution.

### Step-by-Step Solution:

1. **Identify the Dimensions of the Cuboid**:
- Length (l) = 5 cm
- Breadth (b) = 4 cm
- Height (h) = 3 cm

2. **Determine the Smallest Face**:
- The smallest face is the one with dimensions 3 cm (height) and 4 cm (breadth). This face is a rectangle with dimensions 3 cm and 4 cm.

3. **Find the Diagonal of the Smallest Face**:
- To find the diagonal (d) of the rectangle, we can use the Pythagorean theorem:
\[ d = \sqrt{(height)^2 + (breadth)^2} \]
\[ d = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ cm} \]

4. **Identify the Area of the Sliced Section**:
- The sliced section forms a rectangle with one side being the diagonal (d) and the other side being the height of the cuboid (h).
- The area (A) of the sliced section can be calculated as:
\[ A = d \times h \]
\[ A = 5 \text{ cm} \times 5 \text{ cm} = 25 \text{ cm}^2 \]

5. **Conclusion**:
- Therefore, the surface area of the sliced section is \( 25 \text{ cm}^2 \).

### Final Answer:
The surface area of the sliced section is \( 25 \text{ cm}^2 \).

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