Difference between revisions of "2024 AMC 8 Problems/Problem 22"
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==Solution 2== | ==Solution 2== | ||
There are about <math>\dfrac{1}{0.015}=\dfrac{200}{3}</math> "full circles" of tape, and with average circumference of <math>\dfrac{4+2}{2}\pi=3\pi.</math> <math>\dfrac{200}{3}*3\pi=200\pi, </math> which means the answer is <math>600.</math> | There are about <math>\dfrac{1}{0.015}=\dfrac{200}{3}</math> "full circles" of tape, and with average circumference of <math>\dfrac{4+2}{2}\pi=3\pi.</math> <math>\dfrac{200}{3}*3\pi=200\pi, </math> which means the answer is <math>600.</math> | ||
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==Video Solution 1 by Math-X (First understand the problem!!!)== | ==Video Solution 1 by Math-X (First understand the problem!!!)== | ||
Revision as of 14:54, 26 January 2024
Contents
Problem 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.
(A) 
(B) 
(C) 
(D) 
(E) 
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" is 
. Therefore, the average circumference is 
. Multiplying 
gives 
.
-ILoveMath31415926535
Solution 2
There are about 
"full circles" of tape, and with average circumference of 
which means the answer is 
Solution 3
Video Solution 1 by Math-X (First understand the problem!!!)
https://youtu.be/cMgngeSmFCY?si=Ngh2w5-AAuP38GZk&t=34
~Math-X
