How do I calculate the diameter of a cardboard roll?
A simpler route to the answer is to take a slice though the roll and consider its area. The edge of the ribbon has area 25m times 0.01 mm which is 25,000 mm times 0.01 mm which is 250 square mm. The final roll is to have diameter 10 cm, radius 5 cm or 50 mm, therefore sectional area (pi times r-squared) of 2500 times pi square mm. So the cardboard roll has sectional area of (2500pi -250) square mm, which comes out as 7603.98 square mm. Divide by pi and take square root, giving a radius of 49.1978 mm which is equivalent to a diameter of 9.83956 cm.
