Answer
2970 balloons are required to lift the person.
Work Step by Step
We can find the volume $V$ of one balloon as:
$V = \frac{4}{3}\pi~r^3$
$V = \frac{4}{3}\pi~(0.165~m)^3$
$V = 0.0188~m^3$
We can find the buoyant force on each balloon. The buoyant force is equal to the weight of the air that is displaced by the volume of one balloon. Let $\rho_a$ be the density of air.
$F_B = \rho_a~V~g$
$F_B = (1.29~kg/m^3)(0.188~m^3)(9.80~m/s^2)$
$F_B = 0.2377~N$
Ignoring the weight of the balloons, the total buoyant force on all the balloons must be at least equal to the person's weight ($M~g$). We can find the number of balloons $n$ which are required.
$n~F_B = M~g$
$n = \frac{M~g}{F_B}$
$n = \frac{(72~kg)(9.80~m/s^2)}{0.2377~N}$
$n = 2970$
Therefore, 2970 balloons are required to lift the person.
