Water Bottle Case Study

Rationale

This exploration is about the optimization of a water bottle, that is, to find out the volume of water contained in a bottle and the surface area of plastic of the bottle and try to reduce the plastic without affecting the volume. Finally, I will evolve why companies don't just use the bottle design with the most volume of water and the least amount of plastic if they are concerned with the environment and want to save themselves some money.

The reason for which I chose this topic is that I am personally very engaged with the issue of saving the planet and not polluting. My school has many water bottles lying around, and as they are plastic, they will take an average of 450 years to decompose if no-one picked them up and recycled them. It

The reason the bottles are underfilled is that they are 'first preloaded with CO2 in order to stabilise the pressure' (Gerolstiner water preduction system).

Now, I will use the same functions to calculate the lateral surface area of plastic used in these bottles using the equation SA=2π∫_a^b▒〖f(x)dx〗.

-SA1=2π∫_0^3▒〖(-0.1x^2+0.35x+2.8)dx=57.02〖cm〗^2 〗

-SA2=2π∫_3^9.5▒〖(-0.033x^2+0.423x+1.98)dx=131.45〖cm〗^2 〗

-SA3=2π∫_9.5^13▒〖(0.025x^2-0.562x+6.0875)dx=64.97〖cm〗^2 〗

-SA4=2π∫_13^19▒〖(-0.13x^2+3.97x-27)dx=107.44〖cm〗^2 〗

If we discount the dimpled shape of the bottom, it could be modeled by a circle. The radius would be f(0), so its area would be π[f(0)]^2≈24.63〖cm〗^2. Assuming that the bottom is the same thickness, the total surface area of plastic used to make each Harrogate water bottle is about 385.51cm2

Photos of bottle types to show variety (why are they