Answer:
a) 6 complete times
b) 19.3%
Step-by-step explanation:
In every turn, the diameter of the twine increases 1 cm.
After the first turn, there is a total wrapped of 3.14*2=6.3 cm.
After the second turn, we have wrapped 6.3+3.14*(2+1)=15.7 cm.
If we continue with these algorithm, we have that after the 6th turn we have 84.8 cm wrapped. <em>This is the last complete turn.</em>
T = 0 D = 2 cm. Wrapped = 6.3 cm. Total wrapped = 6.3 cm.
T = 1 D = 3 cm. Wrapped = 9.4 cm. Total wrapped = 15.7 cm.
T = 2 D = 4 cm. Wrapped = 12.6 cm. Total wrapped = 28.3 cm.
T = 3 D = 5 cm. Wrapped = 15.7 cm. Total wrapped = 44 cm.
T = 4 D = 6 cm. Wrapped = 18.8 cm. Total wrapped = 62.8 cm.
T = 5 D = 7 cm. Wrapped = 22.0 cm. Total wrapped = 84.8 cm.
T = 6 D = 8 cm. Wrapped = 25.1 cm. Total wrapped = 110 cm.
There are left (100-84.8) = 15.2 cm to wrap around the twine, which has a 25.1 cm diameter by now.
The perimeter of the twine is 3.14*25.1=78.8 cm.
The percentage of a complete circle that the last wrapping of the twine will make is:
P = 15.2/78.8 = 0.193 = 19.3%
