Math Question: Josiah has a mass of 75 kg and wants to know how many helium-filled balloons it would take to fly. The density of helium is about 1 kg / m^3 less than regular air, which means a cubic meter of helium can lift about 1 kg. Fully inflated, a balloon has a diameter of 0.3 m and can be modeled as a sphere. He neglects the mass of the balloon in his calculations. About how many balloons would it take to lift Josiah

The first step is to find out how much air one balloon can hold. For that, we need the formula for the volume of a sphere which is V =(4/3)(pi)(r^3). We are given the diameter of 0.3 and the radius r is 1/2 of that or 0.15 m. Let's put that in the formula, so V=(4/3)(pi)(0.15^3). That gives a volume of 0.014 cubic meters for one balloon. This means that one balloon can lift about 0.014 kg. So if Josiah has a mass of 75/kg and each balloon can lift 0.014 kg, divide B=75/.0014 = 5,357. Josiah will need 5,358 balloons to lift off.
Answered On 04/19/2020 21:29