Hi guys!
I hope you can help me out. It's for my work! Here are 2 questions:

1) On a lathe, I need to know an angle for the taper. It boils down to
this:
Length = 2cm
Taper = .5mm (and some others too).

So what is the formula? It seems to be a right angled triangle, with
one length 20mm and one length .5mm, so what does that make the small
angle? (Also the actual formula would be useful as I need it for other
tapers too.)

2) I have to measure the internal dimentions of a tube with an
iregular surface. So, I want to know the crossectional areas. At
regular intervals down the length of the tube, I will take a number of
measurements of diameter. For example, at 5 cm down the tube, I will
take, let's say north south diameter, east west, north-east
south-west, etc. Perhaps 6 or 8 such diameters. If it were a circle of
course they'd all be the same measurement. But it is irregular. What I
want to do is actually work out the area. What formula can I use to
work it out? I am no mathematician, but, I figure if I merely average
out the diameters it will give me an erroneous result. But I feel sure
there must be a way to work this out.

Thank you very much!
Best wishes
Justin