So Im a little lost on how to start looking for a solution here...

Given that you have a spherical balloon made of lead with the shell being .1mm thick. And filled with Helium.

What is the volume required for it to float?

P=10^5Pa
T=300K

What diameter is the balloon?

What is P and T? Is this the temp and pressure of the atmosphere that the baloon is foat in? You would set the weight of the lead sphere = weight of air displaced. If we assume that the interior of the lead balloon is a vacuum, then the total weight of the balloon is:


W_{Balloon} = 4 \pi r^2 t \rho _ {Lead}


where r is the radius, t is the thickness, and \rho _{Lead} is the density of lead. Set this equal to the weight of air that the balloon displaces:


W _{Air} = \frac 4 3 \pi r^3 \rho _{Air}



Use the ideal gas law to calclulate the density of the air:

PV = nRT, or n/V = P/RT. Multiply this by the molecular weight of air to find the air's density given P and T.

Only other unknown is the density of lead - you must have a table where you can look that up.