The sum of the length, breadth, and height of a cuboid box is 20 cm and the total surface area of cuboid is 256 sq. cm. What is the maximum length (in approximate) of a stick that can be placed inside the cuboid box?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 12 cm.
l + b + h = 20
2(lb + bh + hl) = 256
(l + b + h)2 = l2 + b2 + h2 + 2(lb + bh + hl)
⇒ 202 = l2 + b2 + h2 + 256
⇒ 400 = l2 + b2 + h2 + 256
⇒ l2 + b2 + h2 = 400 - 256 = 144
Diagonal (d) = √(l2 + b2 + h2) = √144 = 12
Hence, the maximum length of a stick that can be placed inside the cuboid box is 12 cm.