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If you were to rap around 10m of tape (1mm thick) around a 10cm radius tube stacking on one another. Then how many rolls of tape would there be at the end. And if you were to rap around tape 10 times on the same sized tube, how long would that 1mm thick tape be. I also want the formulas for both. It cant be Length of tape divided by circumfirence because the tube gets thicker after every roll.
- Anonymous1 decade agoFavorite Answer
Do you mean how many times will it wrap around?
Every time you wrap the tube will be 2 mm thicker. You can use calculus for this or just add them up. 10 meters = 1000 cm
1st wrap - c1 = 2 pi r = 2 pi 10 = 62.832 cm
2nd - c2 = 2 pi 11 = 69.115, total = 131.947
3rd - c3 = 2 pi 12 = 75.398, t = 207.345
4th - c4 = 2 pi 13 = 81.681, t = 289.026
5th - c5 = 2 pi 14 = 87.965, t = 376.991
6th - c6 = 2 pi 15 = 94.248, t = 471.239
7th - c7 = 2 pi 16 - 100.531, t = 571.770
8th - c8 = 2 pi 17 = 106.814, t = 678.584
9th - c9 = 2 pi 18 = 113.097, t = 791.681
10th - c10 = 2 pi 19 = 119.381, t = 911.062
11th - c11 = 2 pi 20 = 125.664
Only need 1000 - 911.062 = 88.938
So total wraps around = 11 88938/125644 or about 11.7 times