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Particular apologies to Jim30, I am seeing words that aren't even in the message!

If I were submitting this puzzle, I would definitely be sending in RADIUSONE highlighted. The misprints in clues intend the solver to look for the diameter of the circle to find information. Then it should be read "take the value of radius to be 1". Reading around the circle gives "Area (=) 3.1415" which of course the calculation of area does give you when r = 1. It appears that the TWO is a total red herring!

I think unclued has summarised this well and do believe it is what the setter intended. Whether the TWO is a deliberate red herring is debatable.

Still don't like the expression RADIUSONE to mean let radius take the value of 1. To me, mathematically, it suggests a subscript.

A circle of radius one has area 3.1415... seems perfectly OK to me.

Yes, I also think it's quite natural, the numerical equivalent of "a circle of radius r inside a square of side a ..." etc.

I am sorry everybody but I am really struggling, perhaps someone can relieve my Listerneritis. It’s the message that is confusing me - DIAMETER IS INSIDE A CIRCLE. It is simply ‘IS’ that throws me completely. DIAMETER INSIDE OF A CIRCLE would leave me in no doubt but the IS seems to tell me that I am looking for something. Am I just reading too much into it?

jim360 and kilgore trout,

Yes, I agree with you both. In those contexts, radius one is fine and is quite normal in, for example, examination questions - I ought to know (!)

However the stand-alone phrase "radius one" means very little to me without more. It could simply define a variable as 'radius' sub 1.

nick,

I wouldn't read too much into the phrase other than to highlight the circle and the relevant diameter.

The representation of the equation isn't very accurate anyway. If the radius is one unit, the area is not pi units, but pi square units, which is why the two seems such an tempting word to highlight instead of one. However, the theme is really about a relationship, so perhaps the setter should be allowed some latitude.
Like nick, I was puzzled by 'is', which turns the message from a description of the 37 cells into a slightly puzzling statement. I think it's only purpose is to help use all the down clues, though I don't see why the setter couldn't have gone for clarity and made the first and last clues normal, avoiding 'is' altogether.