$20\mathrm{.}4.$ A $2-$in copper cylinder, $6$ in length, at a uniform temperature of $200$ F $,$ is plunged vertically into a large tank of water at $50$ F $.$

a$.$ How long will it take for the outside surface of the cylinder to reach $100F?$

b$.$ How long will it take for the center of the cylinder to reach $100$ F $?$

c$.$ What is the surface temperature when the center temperature is $100$ F $?$ Heat transfer from ends of the cylinder may be neglected.