Consider we have a roll of paper with the size of 5 cm in diameter and 10 cm in width. If the thickness of the paper sheet is 0.05 cm, and the rolling has been started from the point zero (the internal reel is 0cm), how can we calculate the length or area of the whole paper sheet?
Asked
Active
Viewed 1,209 times
0
Yoria
- 81
-
The duplicate question has extensive discussion. – Ross Millikan Oct 03 '17 at 18:54
1 Answers
0
First, let's find the number of wraps: $2.5/0.05=50$. Now, the radius of the first wrap will be 0.05, the second: $0.05\cdot 2$, $k-th$ radius will be $0.05k$. The area of one wrap will be $2 \cdot 0.05 \cdot k \cdot \pi \cdot 10=k\pi$. So we have area $$A=\sum_{k=1}^{50}k\pi=25\cdot 51 \cdot \pi$$
Vasili
- 10,690
-
both of these answers are approximations to the correct answer, but only approximations - the roll is a spiral and not made of concentric rings. The top profile of the roll is not a circle! – Sort of Damocles Oct 03 '17 at 18:48
-
I agree that the outer layer may not be the complete circle so it is an approximation but all inner layers should be circular, no? – Vasili Oct 03 '17 at 18:57