Question

The shortest distance a spider should crawl from one corner to the opposite corner of a cubical room of dimensions $3m$ is

• A. $3\sqrt{3}m$
• B. $(3\sqrt{2}+3)m$
• C. $3\sqrt{5}m$
• D. $9m$

Answer 1

Answer: (C)

$3\sqrt{5}m$

To understand the solution clearly, open the cubical box as shown in the figure.
It is given in the question that the spider should crawl from one corner to the opposite corner of the room. The shortest distance from one corner to the other corner is the 3D diagonal.

Let us consider one of the 3D diagonals $CH$. Shortest distance $CH$ is correct but $CH=\sqrt{{CA}^2+{AH}^2}=3\sqrt{2}m$ is not the correct answer for this question because this route is aerial and the spider can only crawl along the ground or walls.

Route, $CH=CA+AH=(3\sqrt{2}+3)m$ is also not correct as it is not the shortest.

Shortest distance to crawl is $CH=\sqrt{{CG}^2+{GH}^2}=3\sqrt{5}m$