UPSC CDS Math Volume and Surface Area Questions

let the dimensions of cuboid are
Length=l
breadth=b
height =h
given area of three faces x,y and z
lb=x⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(1)
bh=y⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(2)
lh=z⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(3)
multiply (1),(2) and (3)
lb×bh×lh=xyz
l2×b2×h2=xyz
(lbh)2=xyz
v2=xyz
since volume of the cuboid= v=lbh