Solve the Problem of Rotating a Strangely-Shaped Slab

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The problem is:
A thin slab of material of uniform density with a total mass 3.0 kg is cut in a strange shape: It is bounded by the curves y=4-x^2 and x=0. Initially it is lying in the xy plane. It is free to rotate about the y axi. A force of 8.0 Newtons is constantly applied perpendicular to the slab at the outer bottom corner. What angle (In radians) has it rotated through after 20 seconds?

A helper on this forum told me to do r^2 dm. However my professor say that this is incorrect and that I need to use the are of the object to answer the problem.

If anybody can help me solve this problem it would be very much appreciated!
 
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