A helium balloon can just lift a load of 790 N. The skin of the balloon has a mass of 1.80 kg. What is the volume of the balloon? (the density of air is 1.29 kg/m³ and the density of helium is 0.179 kg/m³)

74.10 cubic meters

Explanation:

The weught of load, balloon and heilium equals the weight of air displaced.

We know that density is mass per unit volume hence mass is product of density and volume, m=dv where d is density and v is volume

Weight is product of mass and acceleration due to gravity, W=mg=mgv where g is acceleration due to gravity and m is mass. We take g to be 9.81 m/s2

Weight of load=790 N

Weight of ballon = mg = 1.8*9.81

Weight of helium=0.179*9.81*v

Weight of air displaced = 1.29*9.81*v

790 + (1.8*9.81) + (9.81*0.179*v) = 1.29*9.81*v

(1.29-0.179) v*9.81=807.658

10.89891v=807.658

V=74.104474667650

Rounding off, the volume is 74.10 cubic meters