Difference between revisions of "2008 AMC 8 Problems/Problem 18"
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− | ==Problem== | + | == Problem == |
Two circles that share the same center have radii <math>10</math> meters and <math>20</math> meters. An aardvark runs along the path shown, starting at <math>A</math> and ending at <math>K</math>. How many meters does the aardvark run? | Two circles that share the same center have radii <math>10</math> meters and <math>20</math> meters. An aardvark runs along the path shown, starting at <math>A</math> and ending at <math>K</math>. How many meters does the aardvark run? | ||
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<asy> | <asy> | ||
size((150)); | size((150)); | ||
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label("$K$", (20,0), E); | label("$K$", (20,0), E); | ||
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<math> \textbf{(A)}\ 10\pi+20\qquad\textbf{(B)}\ 10\pi+30\qquad\textbf{(C)}\ 10\pi+40\qquad\textbf{(D)}\ 20\pi+20\qquad \\ \textbf{(E)}\ 20\pi+40</math> | <math> \textbf{(A)}\ 10\pi+20\qquad\textbf{(B)}\ 10\pi+30\qquad\textbf{(C)}\ 10\pi+40\qquad\textbf{(D)}\ 20\pi+20\qquad \\ \textbf{(E)}\ 20\pi+40</math> | ||
− | ==See Also== | + | == Solution == |
+ | We will deal with this part by part: | ||
+ | Part 1: 1/4 circumference of big circle= <math>\frac{2\pi r}{4}=\frac{\pi r}{2}=\frac{20\pi}{2}=10\pi</math> | ||
+ | Part 2: Big radius minus small radius= <math>20-10=10</math> | ||
+ | Part 3: 1/4 circumference of small circle= <math>\frac{\pi r}{2}=\frac{10\pi}{2}=5\pi</math> | ||
+ | Part 4: Diameter of small circle: <math>2*10=20</math> | ||
+ | Part 5: Same as part 3: <math>5\pi</math> | ||
+ | Part 6: Same as part 2: <math>10</math> | ||
+ | Total: <math>10\pi + 10 + 5\pi + 20 + 5\pi + 10 = \boxed{E = 20\pi + 40}</math> | ||
+ | |||
+ | == Video Solution == | ||
+ | https://www.youtube.com/watch?v=NJs4rFyXFwQ | ||
+ | —DSA_Catachu | ||
+ | |||
+ | == See Also == | ||
{{AMC8 box|year=2008|num-b=17|num-a=19}} | {{AMC8 box|year=2008|num-b=17|num-a=19}} | ||
+ | {{MAA Notice}} |
Latest revision as of 13:37, 19 October 2020
Contents
Problem
Two circles that share the same center have radii meters and meters. An aardvark runs along the path shown, starting at and ending at . How many meters does the aardvark run?
Solution
We will deal with this part by part: Part 1: 1/4 circumference of big circle= Part 2: Big radius minus small radius= Part 3: 1/4 circumference of small circle= Part 4: Diameter of small circle: Part 5: Same as part 3: Part 6: Same as part 2: Total:
Video Solution
https://www.youtube.com/watch?v=NJs4rFyXFwQ —DSA_Catachu
See Also
2008 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.