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Help with HL maths IA topic on cars and surface of revolution

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My maths teacher suggested the topic of finding the volume and surface area of a car using surface of revolution, and checking if it is optimize using calculus. What I did not understand is how exactly to use surface of revolution.

I thought that the top of a car could act as a part of a semi-circle, but that would only be finding the volume of the top. Does anyone know how I can proceed? Thanks!

 

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When you have a hammer, everything looks like a nail.

You can't be expected to use revolution to find every volume or surface area. Some more advanced techniques are explored in a multivariate calculus course, which you may want to reference. You will have excellent oppprtunity to connect calc and vectors.

 

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