I know how moment of inertia of a disc is calculated using the usual way, but just for fun, I tried this way which is rather giving incorrect answer. I don't know what's the flaw in this and thus would like to have you help me figure out the flaw.
So I imagined that a disc can be taken as a collection of many thin rods with one end joined. The arrangement can be imagined as spokes of a wheel as shown
Now, moment of inertia of a rod about an axis through one end perpendicular to it is $ml^2/3$ where m is mass of rod and l is it's length. Using this moment of inertia of the arrangement which tends to be a disc as number of spokes increases will be simply the sum of moment of inertia of each spoke giving $Ml^2/3$ if the total mass of arrangement is $M$.
Now l is nothing but radius of our disc and thus it gives moment of inertia of a disc as $MR^2/2$.
I don't know what's the problem in my line of reasoning, but the answer is clearly incorrect.