Buoyancy and Archimedes' Principle (Helium ballon and cargo problem)

[Proleague]

Homework Statement

" A spherical balloon has a radius of 7.35 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself."

Homework Equations

So F(b) = (mass of helium + mass of cargo) X 9.8

F(b) = Density of air X volume X 9.8

9.8 cancels out on both sides.

Density of air is 1.29 kg/m^3 so
1.29V = (mass of helium + mass of cargo)

mass of helium = density of helium (.179) X volume

so 1.29V - .179(V) = mass of cargo
V for a sphere = 4/3 (pi) (r)^3 = 1663.2

The Attempt at a Solution

plug that in and I get 1847.8 for the mass, which is WRONG
strangely if I divide that by 2 I get the right answer though... 924, which rounded down would be 920, but I have no idea why id divide it by 2.

I do not know what thing is wrong, and please explain detail. I am an international student.

 

[Borek]

You forgot to include mass of the balloon in your calculations.

 

[Proleague]

hmm... I don't know what you mean. Could you explain more easier to me?
Well.. Actually, I don't know where should I put mass of the balloon.

Could you write a equation exactly include mass of the balloon?

 

[Borek]

Before balloon can lift anything else, it has to lift itself.