The figure above shows a cord around two circular disks. If the radii of the two disks are 80 centimeters and 60 centimeters, respectively, what is the total length, in centimeters, of the cord?
a. 210pi
b. 210pi +280
c. 280pi
d. 280pi +80
e. 280pi +280
Left Circle:
C = 2Ï€r = 2*Ï€*80 = 160Ï€.
Since ∠ABC/360 = 90/360 = 1/4, minor arc AC constitutes 1/4 of the circumference.
Thus, the cord wraps around the remaining 3/4 of the circumference, counter-clockwise from A to C:
(3/4) * 160Ï€ = 120Ï€.
Right Circle:
C = 2Ï€r = 2*Ï€*60 = 120Ï€.
Since ∠DEF/360 = 90/360 = 1/4, minor arc DF constitutes 1/4 of the circumference.
Thus, the cord wraps around the remaining 3/4 of the circumference, clockwise from D to F:
(3/4) * 120Ï€ = 90Ï€.
Connecting cord pieces:
AG + CG + DG + FG = 80+80+60+60 = 280.
Total length = 120Ï€ + 90Ï€ + 280 = 210Ï€ + 280.
The correct answer is
B.
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