Question

A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg/m3 and the density of helium in the balloon is 0.18 kg/m3. The radius of the balloon (when filled) is R = 4.5 m. The total mass of the empty balloon and basket is mb = 123 kg and the total volume is Vb = 0.068 m3. Assume the average person that gets into the balloon has a mass mp = 74 kg and volume Vp = 0.077 m3.What is the volume of helium in the balloon when fully inflated?

Answer 1

V = 381.70 m³

Step-by-step explanation:

ρ air = 1.28 kg / m³

ρ helium = 0.18 kg / m³

R = 4.5 m

Vb = 0.068 m³

mb = 123 kg

To determine the volume of helium in the balloon when fully inflated

V = 4 / 3 π * R ³

V = 4 * π / 3 ( 4.5 m )³

V = 381.70 m³

To determine the mass total

m = ρ helium * V

m = 0.18 kg / m³ * 381.70 m³

m = 68.70 kg

mt = ( 68.70 + 123 )kg

mt = 191.70 kg