A 650 kg weather balloon is designed to lift a 4600 kg package. What volume should the balloon have after being inflated with helium at 0 degrees celcius and 1 atm pressure to lift the total load?The buoyancy force must equal the weight lifted. Let V be the volume.

g*[(He density)* V + 650 kg] = (Air density)*V*g

Cancel out the g's. Assume the outside air density correesponds to the same 1 atm and 0 C. He density is 4 kg/22.4 m^3 and the air density is 29/22.4 kg/m^3

0.179 V + 650 = 1.295 V

Solve for V (in cubic meters)

g*[(He density)* V + 650 kg] = (Air density)*V*g

Cancel out the g's. Assume the outside air density correesponds to the same 1 atm and 0 C. He density is 4 kg/22.4 m^3 and the air density is 29/22.4 kg/m^3

0.179 V + 650 = 1.295 V

Solve for V (in cubic meters)