Answer: 35
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Step-by-step explanation:
To start off, we'll find the circumference of the full circle. We'll ignore the black and yellow sectors.
C = 2*pi*r
C = 2*pi*7
C = 14pi
This is the exact distance around the full circle in terms of pi
However, we don't want the the full circular perimeter. Instead, we only want the portions that are along the black sectors. The yellow sectors have central angle 24 degrees each. This takes up 3*24 = 72 degrees overall because the three regions have equal area and equal central angle.
Subtract that from 360:
360-72 = 288
The yellow regions take up 72 degrees while the remaining black sectors take up a combined 288 degrees.
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Why is 288 useful? Because it helps set up the fraction 288/360 to represent the portion of the perimeter that we care about.
(288/360)*14pi = 35.1858 mm approximately
This rounds to 35 mm