The total surface area of a hollow cuboid is 340 cm². If the length and the breadth of the cuboid are 10 cm and 8 cm respectively, then what is the length of the longest stick that can be fitted inside the cuboid?

$3\sqrt{21}$cm

We know that,

Total surface area = 2[lb + bh + hl]

We have,

The total surface area of the cuboid = 340

Now, according to the question,

= 340 = 2[10 × 8 + 8 × h + h × 10]

= 170 = 80 + 8h + 10h

= 90 = 18h

= h = 5 cm

= The length of the longest stick = diagonal of cuboid

= \(\sqrt {l^2 + b^2 + h^2}\)  = \(\sqrt {100 + 64 + h25}\)  = \(\sqrt {189}\)  = 3\(\sqrt {21}\)  cm