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"Ovoid" is not clearly defined.

In the case of an ellipsoid, the figure is clearly defined, but - just as the circumference of an ellipse - the surface area of an ellipsoid is somewhat difficult to calculate, and can't be expressed in terms of elementary functions.

The Wikipedia article on "ellipsoid" has an approximate formula that you can use.

Both the Wikipedia and Wolfram Alpha have exact formulae; but understanding them requires some advanced math.

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Q: What is Surface area of ovoid?
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