Question

What is the maximum length of a rod that can be placed inside a box having the shape of a cuboid of length $30$ cm, breadth $24$ cm and height $18$ cm?

• A. $30$ cm
• B. $30\sqrt{2}$ cm
• C. $24$ cm
• D. $18\sqrt{5}$ cm

Answer 1

The correct option is B $30\sqrt{2}$ cm

Given, length $=30$ cm, breadth $=24$ cm, height $=18$cm

From the question, we have

Maximum length of the rod $=$ Length of the diagonal of the cuboid
$=\sqrt{l^2+b^2+h^2}$
$=\sqrt{{30}^2+{24}^2+{18}^2}$
$=\sqrt{900+576+324}$
$=\sqrt{1800}$
$=30\sqrt{2}$ cm

Therefore, maximum length of a rod is $30\sqrt{2}$ cm.