Area of the floor of a cubical room is 48 sq. m. The length of longest rod that can be kept in that room in

Options

A. 9 metre
B. 12 metre
C. 18 metre
D. 6 metre

Answer

To find the length of the longest rod that can be kept in a cubical room with a given floor area, we can follow these steps:

### Step 1: Understand the problem
We know that the area of the floor of the cubical room is given as 48 sq. m. Since the room is cubical, all sides of the cube are equal.

### Step 2: Calculate the side length of the cube
The area of the floor (which is a square) can be calculated using the formula:
\[ \text{Area} = \text{side}^2 \]
Let the side length of the cube be \( s \). Therefore, we can write:
\[ s^2 = 48 \]
To find \( s \), we take the square root of both sides:
\[ s = \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \text{ m} \]

### Step 3: Calculate the length of the diagonal of the cube
The longest rod that can fit in the cube is the space diagonal. The formula for the diagonal \( d \) of a cube with side length \( s \) is:
\[ d = s\sqrt{3} \]
Substituting the value of \( s \):
\[ d = (4\sqrt{3})\sqrt{3} = 4 \times 3 = 12 \text{ m} \]

### Step 4: Conclusion
The length of the longest rod that can be kept in the cubical room is:
\[ \boxed{12 \text{ m}} \]

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