​Area of the floor of a cubical from is $$48 m^2$$​. The length of the longest rod that can be kept in that room is​

Correct option is B

Solution

We are tasked to calculate the length of the longest rod that can be kept in a cubical room whose floor area is 48 $$m^2$$​ .

Step-by-Step Solution:

1. Given:

- Area of the floor = 48 $$m^2$$​ .

- The floor is a square since the room is cubical.

2. Find the side length of the cube:

The area of the floor is given by:

​$$\text{Area} = \text{Side}^2$$​

Substituting the value:

​$$48 = \text{Side}^2$$​

Taking the square root:

​$$\text{Side} = \sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3} \, \text{m}$$​

3. Length of the longest rod:

The longest rod that can be kept in a cubical room is its space diagonal, which is given by:

​$$\text{Diagonal} = \sqrt{\text{Side}^2 + \text{Side}^2 + \text{Side}^2} = \sqrt{3 \cdot \text{Side}^2}$$​

Substituting Side = $$4\sqrt{3}$$​ 

​$$\text{Diagonal} = \sqrt{3 \cdot (4\sqrt{3})^2} = \sqrt{3 \cdot 48} = \sqrt{144} = 12 \, \text{m}$$​

Final Answer:

​$$\boxed{12 \, \text{m}}$$​