Question

A roll of tape is $4$ inches in diameter and is wrapped around a ring that is $2$ inches in diameter. A cross section of the tape is shown in the figure below. The tape is $0.015$ inches thick. If the tape is completely unrolled, approximately how long would it be? Round your answer to the nearest $100$ inches.

$300$

$600$

$1200$

$1500$

$1800$

Answer: B

Concepts:circumference estimation

Difficulty rating: 1580

Video solution:

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Written solution:

The tape occupies an annulus with outer radius $2$ inches and inner radius $1$ inch, so its cross-sectional area is $\pi(2^2-1^2)=3\pi.$

When unrolled, this same cross section is a rectangle of thickness $0.015$ inches and length $L.$ Thus $0.015L=3\pi,$ so $L=200\pi\approx628$ inches. Rounded to the nearest $100$ inches, this is $600$ inches.

Thus, B is the correct answer.

2024 AMC 8 Problem 22

Answer: B

Difficulty rating: 1580

Video solution:

Written solution:

Problem 22 in Other Years