I'm doing my Math HL IA on finding the volume and surface area of a frustum (from a cone). I'm determining the volume in three ways, out of which one is integration. I'm calculating the surface area in two ways, one of which uses*integration too. However, though the formula for surface area is out of the HL syllabus, I feel like this is a very simple idea, and might not fulfill the 'Use of Mathematics' criterion as formulae for the volume and S.A. is available online. My Math teacher says this is sophisticated enough, though I feel the opposite. I would like an opinion on this topic and whether I can do anything else to make this topic more sophisticated.
Thanks in advance!
... my heart's just not in it