Math CentralQuandaries & Queries


Question from Emily, a student:

Hi, I was wondering how to calculate the surface area of a cone with an oval as a base (which I think is referred to as an elliptic cone or something like that).

I have the both the maximum and minimum radius as well as the height, but I don't have a slant height and I'm not sure how to calculate it and then calculate surface area. I would really appreciate some help. Thanks!

Hi Emily: Unfortunately this problem is impossible, as the data you have are not sufficient. The volume is easily calculated as $\large \frac{\pi}{3} a \; b\; h,$ but the area depends on how slanted the cone is. Suppose the apex was a million kilometers away sideways from the base but only a meter above it - clearly the area would be very, very large.

Good Hunting!

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