What is the maximum length of a rod which can be kept in a rectangular box with internal dimensions 32 cm x 24 cm x 8 cm.

Given:

The length of the rectangular box = 32 cm

The breadth of the rectangular box = 24 cm

The height of the rectangular box = 8 cm

Maximum length of the rod = Length of diagonal

Length of diagonal = $\sqrt{l^2 + b^2 + h^2}$

$= \sqrt{32^2 + 24^2 + 8^2}\\[1em] = \sqrt{1,024 + 576 + 64}\\[1em] = \sqrt{1,664}\\[1em] = 8\sqrt{26}\\[1em] = 40.79$

Hence, the maximum length of a rod that can be kept in the rectangular box is 40.79 cm.