The length of the longest rod that can be fitted in a cubical vessel of edge `10 c m\ ` long, is `10\ c m` (b) `10\ sqrt(2)\ c m` (c) `10\ sqrt(3)\ c m` (d) `20\ c m`

Explanation

The length of the edges of the cuboid is 10 cm. The length of the longest stick that can be placed in it is equal to the distance from one corner to the corner on the opposite face that lies diagonally opposite to it.

By Pythagorean Theorem

`L=sqrt(10^2+10^2+10^2)`

`L=sqrt(3xx100)`cm

`L=3cm`

The length of the longest stick that can be placed in a cuboid with edges 20 cm is `10sqrt3` cm.

Hence, option (c) is correct.