IA (HL) Help with my IA needed. Initial steps taken.

[Michał H.]

Hi! I'd like to do my IA about a conical tank filled with water at a certain speed. Question; How fast is the water level rising?"

I was wondering how I can apporach it. Any suggestions and help really desired and appreciated.

[maroctam]

Have you done differential calculus yet, more specifically optimisation? Because if you have you'd know that this question is too simple for an IA; a 6-12 page project. I assume you haven't yet, since you're asking the question. If that's the case how far are you into differential calculus? If you've done the basics I can help you solve the problem (for the fun of it) but I highly suggest you talk to your teacher about your IA topic as this is the sort of question you could find on a Math HL paper 1/2 and would be worth 6 marks...

[Michał H.]

I've done everything in calculus. The question appeared as one of suggestions for IA that my teacher hand us out. The thing is I don't know what to start with.

[ctrls]

I suppose you could formulate it as a problem, solve it, then generalize the result. If you can calculate the surface area of the flask and model the rate of flow of water as a function of volume and time, the rest is fairly straightforward.

That alone is too simple though, so you'll probably have to make other considerations. How can you calculate the rate of flow of water? What if there was another hole with water flowing out of the container at the same time? What happens if the shape changes to a pyramid or something similar, where surface area is no longer constant? Where may this be useful?

Also, when you say you have done "everything in calculus," does that also include the options chapter? If so, there's a lot you can do with differential equations to model the system, which would be rather interesting.