The length of the longest rod that can be placed in a cubical room is 8√3cm. What is the volume of the cube?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 512 cm3.
The longest rod must be placed at a diagonal in the room
So,
The diagonal of the cube = a√3
⇒ 8√3 = a√3
⇒ a = 8 cm
Now,
The volume of the cube = a3
⇒ (8)3
⇒ 512 cm3