To estimate the radius of a helium balloon needed to lift a total weight of 180 kg, including the balloon's weight, the density of air must be considered alongside the density of helium, which is 0.179 kg/m^3. The buoyant force equation, F = ρgV, is crucial for calculations, where V is the volume of the balloon. The initial calculation suggests a radius of 3.22 meters, but this does not account for the density of air, which is essential for accurate buoyancy calculations. Without knowing the surrounding air density, the problem cannot be solved correctly, as a balloon would not float in a vacuum regardless of its size. Accurate calculations require both the density of helium and the density of the air for effective lift.
