2024 AMC 8 Problem 22
Attempt Problem 22 of the 2024 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
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.
Answer: B
Small hint:
The tape occupies an annulus with outer radius and inner radius
Big hint:
Area of tape cross-section equals thickness times total length
Video solution:
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Written solution:
The tape occupies an annulus with outer radius inches and inner radius inch, so its cross-sectional area is
When unrolled, this same cross section is a rectangle of thickness inches and length Thus so inches. Rounded to the nearest inches, this is inches.
Thus, B is the correct answer.
Problem 22 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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- 1991 AMC 8
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- 1993 AMC 8
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- 1998 AMC 8
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