Answer
$m=899.61kg$
Work Step by Step
First we calculate the volume of the balloon:
$V=\frac{4\pi r^3}{3}=\frac{4\pi (12m/2)^3}{3}=904.78m^3$
Then the bouyancy force is:
$F_{b}=\rho_{air}gV=1.16\frac{kg}{m^3}*9.81\frac{m}{s^2}*904.78m^3=10296.03N$
Knowing the bouyancy force, the maximum mass will be:
$m_{max}=\frac{F_{b}}{g}=\frac{10296.03N}{9.81\frac{m}{s^2}}=1049.54kg$
The mass of helium is:
$m_{He}=\rho_{He}*V_{He}=\frac{1.16}{7}\frac{kg}{m^3}*904.78m^3=149.93kg$
Then the maximum amount of load will be:
$m=m_{max}-m_{He}=1049.54kg-149.93kg=899.61kg$
