Roll of Tape
Source: 2024 AMC 8 #22
October 20, 2024
2024 AMC 8AMC 8
Problem Statement
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.[asy]
/* AMC8 P22 2024, revised by Teacher David */
size(120);pair o = (0,0);
real r1 = 1;
real r2 = 2;filldraw(circle(o, r2), mediumgray, linewidth(1pt));
filldraw(circle(o, r1), white, linewidth(1pt));draw((-2,-2.6)--(-2,-2.4));
draw((2,-2.6)--(2,-2.4));
draw((-2,-2.5)--(2,-2.5), L=Label("4 in."));draw((-1,0)--(1,0), L=Label("2 in.", align=(0,1)), arrow=Arrows());draw((2,0)--(2,-1.3), linewidth(1pt));
[/asy]