Max Weight for Helium Balloon: Simple Buoyancy Problem Solution

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The discussion revolves around calculating the maximum mass that can be attached to a helium balloon without it sinking. The balloon has a diameter of 25 cm and a mass of 0.900 g. The user attempted to equate the buoyant force and the gravitational force to find the attachable mass, initially calculating it as 7.5 g but questioning the accuracy. After multiple calculations, the user confirmed the mass as approximately 7.45 g, attributing discrepancies to different constants used compared to the textbook. Ultimately, the user recognized their error as a simple mistake in constants rather than a fundamental misunderstanding of the buoyancy problem.
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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?
 
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Still looking for some help. I've run the calculation several times and keep get 7.45g...
 
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.
 
I was right...I just had different constants than the book...

Dumb mistake.
 

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