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?
(B) 210π+ 280
(D) 280π + 80
(E) 280π+ 280
A chord (or a thread) is wrapped around the two disks as shown. The length of the thread is
Part of circumference of bigger disk + the two intersecting straight lines + Part of circumference of smaller disk
Length of the two straight lines: We see from the figure that there are 2 squares. The length of the straight lines will be 80 + 60 + 80 + 60 = 280
Part of circumference of bigger disk: The arc that forms the 90 degree angle is not included so the rest of it makes 270 degree angle. Circumference = (270/360) * 2*\pi*80 = 120*\pi
Part of circumference of smaller disk: The arc that forms the 90 degree angle is not included so the rest of it makes 270 degree angle. Circumference = (270/360) * 2*\pi*60 = 90*\pi
Total length of chord = 280 + 120*\pi + 90*\pi = 280 + 210*\pi
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