A $0\mathrm{.}72-$m$-$diameter solid sphere can be rotated about an axis through its center by a torque of $10\mathrm{.}8$ m$-$N$.$ This torque causes the sphere to accelerate uniformly from rest through a total of $180$ revolutions in $15\mathrm{.}0$s$.$ a$)$ Calculate the angular acceleration of the sphere b$)$ Using the rotational form of Newton's Second Law, determine the moment of inertia of the sphere. c$)$ Finally, determine the mass of the sphere.