Let the height of this cuboid be h. ⇒ Total surface area = 2[l × b + b × h + h × l] ⇒ 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 ⇒ The length of the longest stick = √ (l2+b2+h2) = √ (100+64+25) = √189 ⇒ The length of the longest stick = 3√21 cm ∴ The length of the longest stick that can be fitted inside the cuboid is 3√21 cm.