UPSC 2014 CDS II Math Paper

Let the length, breadth and height of the cuboidal box be l units, b units and h units, respectively
l × b = x......(1)
b × h = 4x...(2)
h × l = 9x....(3)
Multiplying (1), (2) and (3), we get
l2×b2×h2=x×4x×9x
⇒(l×b×h)2=36x3
⇒ l×b×h
⇒√36x3=6x

3

2

cubic unit
Thus, the volume of the box is 6x

3

2