Question : The sum of the length, breadth, and height of a cuboid box is 20 cm and the total surface area of a cuboid is 256 sq. cm. What is the maximum length (in approximate) of a stick that can be placed inside the cuboid box?
Option 1: 16 cm
Option 2: 24 cm
Option 3: 32 cm
Option 4: 12 cm
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Correct Answer: 12 cm
Solution :
The sum of the length, breadth, and height of a cuboid box is 20 cm.
⇒
The total surface area of the cuboid = 256 sq. cm.
⇒
⇒
The maximum length of a stick that can be placed inside the cuboid is the diagonal of the cuboid and
Diagonal of cuboid =
Using formula (a + b + c)
2
= a
2
+ b
2
+ c
2
+ 2(ab + bc + ca), we get,
⇒
⇒
⇒
Hence, the correct answer is 12 cm.
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