How Much Helium Can a 11m Diameter Balloon Hold and What Can It Lift?

[annas425]

A spherical helium balloon 11 m in diameter is at ambient temperature and pressure, 15 degrees Celsius and 100 kPa. How much helium does it contain? It can list a total mass of balanced atmospheric air. How much mass of the balloon fabric & cage can then be lifted?

Here is my work but I'm unsure if it's correct. If someone could let me know I would really appreciate it. I also don't know how to answer the second part of the problem at all. Thanks in advance!

r = 5.5 m
T = 15°C = 288.15 K
P = 100 kPa = 100 kN/m
R = .287 kN m/kg K

m = PV/RT = 842.69 kg Helium

 

[haruspex]

m = PV/RT = 842.69 kg Helium

You seem to have hybridised two formulae:
PV = mR_specT
PV = nRT
where m is mass, n is number of moles, and R_spec is a constant specific to the gas.

 

[Chestermiller]

What did you get for the volume of the balloon?

Does it really make sense to you that a balloon of this volume can hold close to a metric ton of helium at atmospheric pressure?

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