Maths Olympiad Prep

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Geometry Difficulty 2.8 Junior Find the answer

A roll of tape is 44 inches in diameter and is wrapped around a ring that is 22 inches in diameter. A cross section of the tape is shown in the figure below. The tape is 0.0150.015 inches thick. If the tape is completely unrolled, approximately how long would it be? Round your answer to the nearest 100100 inches.

Pick one

Solution

The roll of tape is 1/0.015=1/0.015=66 layers thick. In order to find the total length, we have to find the average of each concentric circle and multiply it by 6666. Since the diameter of the small circle is 22 inches and the diameter of the large one is 44 inches, the "middle value" is 33. Therefore, the average circumference is 3π3\pi. Multiplying 3π663\pi \cdot 66 gives (B)600(B) \boxed{600}.
-ILoveMath31415926535

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