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[Curlytek]

This nice little problem can be done using two scale diagrams, one of the side on view similar to devjoes, and one of the top down view showing the max size of four circles in a bigger circle....and then you only need to do two simple pieces of maths: 1) work out the dimensions of the cone (or, the triangle in the 2D diagram) with a bit of pythag, and 2) work out how far from the centre line the chocolate scoop needs to be using a simple ratio from the top down view.

Be precise using a nice drawing package that lets you define the dimensions of the objects nicely, line up the edges well and presto, you can take your answer straight from the picture.

[Dragonscales]

Bloody hell... Whipsmart don't care about their customers, do they? Making us figure out the exact measurements of ice-cream. I wouldn't know - I would have eaten it before the question started.

Ben

[almagest]

No, I don't think this is a nice little problem at all! The exact solution is:

[crovax1234]

Noone ever said it was a pretty equation. Also, please spoiler tag that equation.

[rosemary]

for anyone who is still struggling, I don't know if this will help but the key to the drawings is

[fretty]

That's a good point, rosemary, because I use these facts often, I take them as obvoius. That's why there are lots of people stuck with this.

There is one thing though, how come you couldn't solve the end equations, I only ended up with simple trig equations and one quadratic at the end (which was easily solved using the formula).

[Platinumflux]

Had to admit, I panicked when I saw the answer would involve trig!
But drew the solution on Coreldraw and got the answer in 5 minutes!
My first answer was

[jerethdagryphon]

 alternate route