2024 AMC 8 Problems/Problem 22: Difference between revisions
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==Problem 22== | ==Problem 22== | ||
A roll of tape is <math>4</math> inches in diameter and is wrapped around a ring that is <math>2</math> inches in diameter. A cross section of the tape is shown in the figure below. The tape is <math>0.015</math> inches thick. If the tape is completely unrolled, approximately how long would it be? Round your answer to the nearest <math>100</math> inches. | |||
(A) <math>300</math> (B) <math>600</math> (C) <math>1200</math> (D) <math>1500</math> (E) <math>1800</math> | |||
==Solution== | ==Solution== | ||
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> | ||
Revision as of 16:28, 25 January 2024
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
There are about 
"full circles" of tape, and with average circumference of 
which means the answer is 
