Ok, well despite not getting an answer on the DataTables help forum, this appears to have been a known issue, addressed with this Git commit:

https://github.com/DataTables/DataTables/commit/77343b72cb035e1ceba387335136f010282c0940

Solution: download the commit or link to the latest nightly build via the CDN.

How to fix "g.aoColumns[a.aaSorting[f][0]] is undefined" errors after updating dataTables and ColReorder plugins?
I was given the following question:

A wine cask has a radius at the top of $30 cm$ and a radius at the middle of $40 cm$.
The height of the cask is $1m$.
What is the volume of the cask in litres, assuming the shape of the side is parabolic?

I have to come to parabolic function of

$$y = \frac{-1}{250}(x-50)^2+40$$

The derivative of $y$ is:
$$\frac{dy}{dx} = \frac{2}{5} - \frac{x}{125}$$

Then I integrate and end up with an expression the length of $\pi$. Am I on the right track?
