Question

The maximum length of a pencil that can be kept in a rectangular box of dimensions $8cm\times 6cm\times 2cm$, is________.

• A. $2\sqrt{13}$cm
• B. $2\sqrt{14}$cm
• C. $2\sqrt{26}$cm
• D. $10\sqrt{2}$cm

Answer 1

Answer: (C)

$2\sqrt{26}$cm

Here, $l=8cm,b=6cm,h=5cm$

In this question we need to calculate the diagonal of cuboid, which is $=\sqrt{l^2+b^2+h^2}$

$\therefore$ Diagonal of cuboid $=\sqrt{8^2+6^2+2^2}$

$\therefore$ Diagonal of cuboid $=\sqrt{64+36+4}$

$\therefore$ Diagonal of cuboid $=\sqrt{104}$

$\therefore$ Diagonal of cuboid $=2\sqrt{26}cm$