# Math Question???????

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.

Relevance
• Anonymous

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