weight of balloon?

Question

How much does a helium balloon weigh? Assume that you have a spherical weather balloon of radius 1.49 m. Use the value 0.198 kg/m^3 for the density of helium, since the density of helium varies with temperature. Assume that the mass of the skin of the balloon is 0.774 kg. To TWO DECIMAL PLACES, what is the weight of the balloon in pounds? Please use the conversion factor 2.20 lb = 1 kg.

Answer 1

The volume of a sphere is given as,
4/3 * pi * r^3
If the radius (r) is 1.49 meters then the balloon would have a volume of 13.86 cubic meters.

Density = mass / volume
mass = Density * volume
We are given the density of Helium and we just calculated its volume so we can now solve for the Helium's mass,
mass = 0.198 kg/m^3 * 13.86 m^3
mass = 2.74 kg
To this mass (of the Helium), the mass of the balloon material must be added, 2.74 kg + .774 kg = 3.514 kg total mass
Total mass = 3.514 kg

Weight = mass * gravity
W = mg
where g is the gravitational acceleration, which will will assume to be 9.81 m/s^2
Calculating the weight of the balloon is now simply a matter of plugging in the values into the equation,
W = 3.514 kg * 9.81 m/s^2
W = 34.47 Newtons
or if one insists on using the unit of pounds-force,
W = 3.514 kg * 2.20 lbf / kg
W = 7.73 lbf

Answer 2

First volume of sphere is: 4/3 * pi * r^3
given radius 1.49 m, volume is 4/3 * 22/7 * 1.49^3 = 13.8619 m^3

Since helium weighs 0.198 kg for each m^3, and we have 13.8619 m^3, therefore weight of helium is
0.198 * 13.8619 = 2.7447 kg

Given mass of skin of baloon is 0.774 kg

Total weight of balloon is:
weight of skin + weight of helium = 0.774 + 2.7447 = 3.5187 kg

Using 2.20 lb = 1 kg,

Weight of baloon in lb = 3.5187 * 2.20 = 7.7410 lb