Answer
$r=1.07cm$
Work Step by Step
$PV=nRT$
$P_{bottom}=\rho gh=(1.0\times10^3\frac{kg}{m^3})(9.8\frac{m}{s^2})(41.0m)=401800N$
$nR=\frac{PV}{T}=\frac{(3.97atm)(1.0\times10^{-6}m^3)}{(5.5^oC+273)}=1.42\times10^{-8}$
$\frac{P_tV_t}{T_t}=\frac{P_bV_b}{T_b}$
$V_t=\frac{P_bV_bT_t}{T_bP_t}=\frac{(3.97)(1.77\times10^{-6}m^3)(18.5^oC)}{(5.5^oC)(1atm)}\times\frac{3}{4\pi r^3}$
$V_{top}=5.63cm^3$
$r=1.07cm$
