Find the mass of a uniform solid cylinder which is mounted so that it can rotate freely (i.e., without friction) about a fixed axis that passes through its center and runs along the length of the cylinder. This is not a simple project because for one thing, that cylinder is heavy! Also you don't want to risk removing the heavy cylinder from its mounting for fear of damaging its expensive and delicate low-friction mounting system. So you devise a way around the problem. You first wrap a light (effectively massless) inextensible string around the cylinder. You then hang a mass of 12kg from one end of the rope and let the mass fall. As the mass falls, it causes the string to unwrap and the cylinder to rotate. You measure the time taken for the 12 kg mass, starting from rest, to fall a distance of 80cm and find it to be 3.6 seconds. You also measure the radius of the circular cross-section of the cylinder and obtain a value of 24cm. Using this information, you calculate the mass of the cylinder. Your boss is highly impressed by your ingenuity and raises your salary. What value did you get for this mass?
Your numbers are mostly correct - I only find small numerical discrepancies with my numbers, but there is some confusion about the moment of inertia and calculations.
If I may, I would suggest modifying what you did in the following form:
Write only formulas first, and substitute the numbers at ...