A $10\mathrm{.}9-$kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of $10\mathrm{.}2$ m$/$s$,$ determine the following.

$($a$)$ the translational kinetic energy of its center of gravity

$($b$)$ the rotational kinetic energy about its center of gravity

$($c$)$ its total kinetic energy