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?
Answer & explanation
Correct answer: option 3
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