Max Weight for Helium Balloon: Simple Buoyancy Problem Solution

[ChemIsHard]

Homework Statement

A 0.900 g balloon is filled with helium gas until it becomes a 25.0 cm-diameter sphere.
What maximum mass can be tied to the balloon (with a massless string) without the balloon sinking to the floor?

Homework Equations

Fb=VSphere*Pair*Gravity
Fg=Vsphere*Phelium*Gravity

The Attempt at a Solution

I tried to set them equal to each other (so that the net force is 0) and found that...

Vsphere(Phelium-Pair)*9.8-0.0009kg*9.8(mass of ballon)=Mass attachable/9.8

I got 7.5g but that's wrong. Anyone know where I messed up my process?

 

[ChemIsHard]

Still looking for some help. I've run the calculation several times and keep get 7.45g...

 

[ChemIsHard]

I still get 7.45g...weird.

My balloon circumference is 25 cm. The balloon weighs 0.9g. Pair=1.2, PHelium=0.1785

Therefor my radius is 0.125m and my balloon mass is 0.0009kg.

4/3pi(0.125)^3*1.2=Mass+0.0009kg+4/3pi(0.125)^3*0.1785

Mass=0.007457kg=7.5g...

Anyone see where I'm messing up.

 

[ChemIsHard]

I was right...I just had different constants than the book...

Dumb mistake.