Answer
The balloon can lift a cargo of 1045 kg
Work Step by Step
We can find the volume $V$ of the balloon as:
$V = \frac{4}{3}\pi~r^3$
$V = \frac{4}{3}\pi~(7.15~m)^3$
$V = 1531~m^3$
Let $M_c$ be the mass of the cargo. To find the maximum possible mass $M_c$, we can let the buoyant force be equal to the total weight of the balloon and the cargo. Let $\rho_a$ be the density of the air. Therefore;
$(M_c+930~kg)~g = F_B$
$(M_c+930~kg)~g = \rho_a~V~g$
$(M_c+930~kg) = \rho_a~V$
$M_c = \rho_a~V - 930~kg$
$M_c = (1.29~kg/m^3)(1531~m^3) - 930~kg$
$M_c = 1045~kg$
The balloon can lift a cargo of 1045 kg.
