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) $10\sqrt{2}\mathrm{cm}$
(d) $10\sqrt{3}\mathrm{cm}$

Answer 1

(d) $10\sqrt{3}$ cm103√ cm
Length of the longest rod = body diagonal of the vessel
$$\begin{gathered} =\sqrt{3}a \\ =\sqrt{3}\times 10 \\ =10\sqrt{3}\mathrm{cm} \end{gathered}$$