You can make a reel many different dimensions to accommodate the same length of tether. You need to do some calculus to reach exact solution. As an approximation, if you have a 300 meter tether, and the width of the reel will accommodate 30 (8mm) tether-widths, then you have 30 separate spirals each 10 m in length. Then if you say that the inner diameter of the reel is 20cm, then you can solve for the outer diameter by constructing a spiral (calculus) using the dimensions of the tether (8mm diameter, 10m long). Here I found an online calculator for the calculus bit: Calculator for Outside Diameter of Roll of Material
Using the above parameters, the calculator tells me the outer diameter will be ~40cm.

By this method, I’ve approximated that a reel approximately 25cm width x 20cm inner diameter x 40cm outer diameter will hold 300m of tether.

Jacob is right, all the reel dimensions are interdependent and will vary. In addition, I would recommend an inner diameter of no less than 7 inches to make winding easier both on you and the tether in regard to its flexibility and bend radius. If you take the raw volume of the tether (Lpir^2) I would recommend multiplying this by at least 1.5-1.75 to have a comfortable reel volume which will accommodate the tether even if not wound perfectly.