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

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 where the area of the floor is given, we can follow these steps:

### Step 1: Understand the properties of the cube
A cubical room has all sides equal. Let's denote the length of each side of the cube as \( A \).

### Step 2: Relate the area of the floor to the side length
The area of the floor of the cubical room is given as 48 sq.m. Since the floor is a square (because it's a cube), the area can be expressed as:
\[ \text{Area} = A \times A = A^2 \]
Thus, we have:
\[ A^2 = 48 \]

### Step 3: Solve for the side length \( A \)
To find \( A \), we take the square root of both sides:
\[ A = \sqrt{48} \]
This can be simplified:
\[ A = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]

### Step 4: Find the length of the longest rod
The longest rod that can fit in the cubical room is the space diagonal of the cube. The formula for the diagonal \( D \) of a cube with side length \( A \) is:
\[ D = A\sqrt{3} \]
Substituting the value of \( A \):
\[ D = (4\sqrt{3})\sqrt{3} = 4 \times 3 = 12 \]

### Final Answer
Thus, the length of the longest rod that can be kept in the room is \( 12 \) meters.

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