What is the maximum length of a pencil that can be placed in a rectangular box of dimensions

Question:

What is the maximum length of a pencil that can be placed in a rectangular box of dimensions (8 cm × 6 cm × 5 cm)?
(a) 8 cm
(b) 9.5 cm
(c) 19 cm
(d) 11.2 cm

Solution:

(d) 11.2 cm
Maximum length of the pencil =  diagonal of the box

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

$=\sqrt{8^{2}+6^{2}+5^{2}} \mathrm{~cm}$

$=\sqrt{64+36+25} \mathrm{~cm}$

$=\sqrt{125} \mathrm{~cm}$

$=11.2 \mathrm{~cm}$

 

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