Question

Chloe and Libby want to tie Ryan to a bunch of approximately spherical helium balloons of diameter 0.3m. The volume of each balloon can be approximated using the formula 4r³. Given that 1 litre of helium can lift 1g, and that Ryan weighs 5 stone and 5lb, estimate how many balloons they need to make him float.

Answer 1

Answer: Aproximately 2,525 balloons

Explanation:

1. Find the volume of a balloon with the formula given in the problem, where
`r` is the radius (
`r=(0.3m)/(2)=0.15m`), then:

`V=4(0.15m)^(3)=0.0135m^(3)`

2. Convert the volume from m³ to lliters by multiplying it by 1,000:

`V=0.0135m^(3)*1000=13.5L`

3. You know that that 1 liter of helium can lift 1 gram and that Ryan weighs 5 stone and 5 pounds. So you must make the following conversions:

1 g=0.0022 lb

From 5 stones to pounds

`(5stone)((14pounds)/(1stone))=70pounds=70lbs`

4. Then Ryan's weigh is:

5lb+70lb=75lb

5. Then, if 1 liter of helium can lift 0.0022 lb, to lift 75 lb (which is the weight of Ryan) they need:

`(75lb*1L)/(0.0022lb)=34,090.90L`

6. Then, to calculate the aproximated number of balloons they need to make him float (which can call
`n`), you must divide the liters of helium needed to lift the weight of Ryan by the volume of a balloon, then the result is:

`n=(34,090.90L)/(13.5L)`

`n=2,525.25`≈2,525 balloons.