Find the steady$-$state temperature $u(r,z)$ in the cylinder depicted in the figure if the lateral side is kept at the temperature $90$ and the top $z=4$ and the base $z=0$ are insulated.

a$)$ None of the above

b$)$ The steady$-$state temperature is $100$

c$)$ The steady$-$state temperature is $0$

d$)$ The steady$-$state temperature is $90.$