2024 AMC 8
Complete problem set with solutions and individual problem pages
A roll of tape is inches in diameter and is wrapped around a ring that is inches in diameter. A cross section of the tape is shown in the figure below. The tape is inches thick. If the tape is completely unrolled, approximately how long would it be? Round your answer to the nearest inches.
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Solution 1
The roll of tape is layers thick. In order to find the total length, we have to find the average of each concentric circle and multiply it by . Since the diameter of the small circle is inches and the diameter of the large one is inches, the "middle value" (or mean) is .
Therefore, the average circumference is . Multiplying gives approximately .
Solution 2
There are about "full circles" of tape, and with average circumference of which means the answer is .
