Moment of Inertia of a body with linearly increasing density?

[easwar2641993]

A thin wire of length L and uniformly density ρ is bent into a circular loop with center at O.The moment of inertia of it about a tangential axis lying in the plane of loop is.
Ans : Mass M is not given,but ρ is given. So M=ρL3->(1) (L3 means L cube,no idea how to post it in that manner!). For a circular loop, we all know the formula for that condition is (3/2)MR square. Applying this in equation for equation (1) will give (3/2)ρL3 x (L square/4∏ square)
This will give 3ρL raised to 5 / 8∏ square.

But my teacher told the answer is 3ρL cube/8∏square.
This is not a home work.This is just a practice for me.
In this,where is my mistake?

 

[mfb]

The wire is thin, not a cube, its volume is not L³ (can be written as [noparse]L³[/noparse], but L^3 is fine, too. Or use LaTeX: [itex]L^3[/itex] becomes $L^3$).
I would expect that ρ is given as line density (kg/m), or the cross-section of the wire has to be given.