Question

The length of the longest rod that can fit in a cubical vessel of side 10 cm,is
(a) 10 cm (b) 20 cm (c) $10\sqrt{2}$cm (d) $10\sqrt{3}$cm

Answer 1

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.

This length is equal to L = $\sqrt{{10}^2+{10}^2+{10}^2}$ cm using the Pythagorean Theorem.

L = $\sqrt{3\times 100}$ cm


=> L = $\sqrt{3}$ cm
The length of the longest stick that can be placed in a cuboid with edges 20 cm is 10 root3 cm
(d) $10\sqrt{3}$ cm