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) $10 \sqrt{3} \mathrm{~cm}$
Solution:
(d) $10 \sqrt{3} \mathrm{~cm}$
Length of the longest rod = body diagonal of the vessel
$=\sqrt{3} a$
$=\sqrt{3} \times 10$
$=10 \sqrt{3} \mathrm{~cm}$