Where r is the radius of balloon.
Here mass of woman = 68 kg
Mass of air displaced by a balloon with volume V = 1.29*V
Mass of helium inside balloon = 0.178*V
Total mass to be lifted by balloon = 68 +0.178*V
Buoyant force = 1.29V-0.178V=1.112V
So we have 1.112 V = 68+ 0.178*V
0.934 V = 68
V = 72.81
\frac{4}{3} \pi r^{3}[/tex]= 72.81
r = 2.59 m
So radius of helium balloon = 2.59 m