Question

chloe and libby want to tie ryan to a bunch of approximatley spherical helium balloons of diameter 0.3m. Thr volume of each balloon can be approximated ising the formula 4r3 given that. 1 litre of helium can lift 1g and that ryan weighs 5stone 5 poundsestimate 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 you have:

$V=4(0.15m)^{3}=0.0135m^{3}$

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

 $V=0.0135m^{3}*1,000=13.5L$

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 conversions shown below:

1 g=0.0022 lb

From 5 stones to pounds:

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

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 $x$ ), you must  divide the liters of helium needed to lift the weight of Ryan by the volume of a balloon, then the result is:

$x=\frac{34,090.90L}{13.5L}=2,525.25$≈2,525 balloons.