Explanation:
It is given that, a solid metal sphere of diameter D is spinning in a gravity-free region of space with an angular velocity of ω.The sphere is slowly heated until it reaches its melting temperature, at which point it flattens into a uniform disk of thickness D/2.
The angular momentum remains conserved in this case. The relation between the angular momentum and the angular velocity is given by :

Where
are moment of inertia of sphere and the disk respectively
Here, volume before = volume after


Initial angular momentum,

..........(1)
Final angular momentum,

............(2)
From equation (1) and (2) :


Hence, this is the required solution.
Kinetic energy
When the rock starts rolling down the hill it has kinetic energy. When the rock gets to the bottom of the hill and stops, it is no longer in motion therefore it no longer has kinetic energy, the energy has been converted back into potential energy.
The answer to your question is 77.3