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

Step-by-step explanation:

1. Find the volume of a balloon with the formula given in the problem, where $r$ is the radius ($r=\frac{0.3m}{2}=0.15m$), 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

$(5stone)(\frac{14pounds}{1stone})=70pounds=70lbs$

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:

$\frac{75lb*1L}{0.0022lb}=34,090.90L$

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:

$n=\frac{34,090.90L}{13.5L}$

$n=2,525.25$≈2,525 balloons.