2007 AMC 8 Problems/Problem 16

Problem

Amanda Reckonwith draws five circles with radii $1, 2, 3, 4$ and $5$ . Then for each circle she plots the point $(C,A)$ , where $C$ is its circumference and $A$ is its area. Which of the following could be her graph?

$\textbf{(A)}$ $[asy] size(75); pair A= (1.5,2) , B= (3,6) , C= (4.5,8) , D= (6,6) , E= (7.5,2) ; draw((0,-1)--(0,16)); draw((-1,0)--(16,0)); dot(A^^B^^C^^D^^E); label("$A$", (0,8), W); label("$C$", (8,0), S);[/asy]$

$\textbf{(B)}$ $[asy] size(75); pair A= (1.5,9) , B= (3,6) , C= (4.5,6) , D= (6,9) , E= (7.5,15) ; draw((0,-1)--(0,16)); draw((-1,0)--(16,0)); dot(A^^B^^C^^D^^E); label("$A$", (0,8), W); label("$C$", (8,0), S);[/asy]$

$\textbf{(C)}$ $[asy] size(75); pair A= (1.5,2) , B= (3,6) , C= (4.5,8) , D= (6,6) , E= (7.5,2) ; draw((0,-1)--(0,16)); draw((-1,0)--(16,0)); dot(A^^B^^C^^D^^E); label("$A$", (0,8), W); label("$C$", (8,0), S);[/asy]$

$\textbf{(D)}$ $[asy] size(75); pair A= (1.5,2) , B= (3,5) , C= (4.5,8) , D= (6,11) , E= (7.5,14) ; draw((0,-1)--(0,16)); draw((-1,0)--(16,0)); dot(A^^B^^C^^D^^E); label("$A$", (0,8), W); label("$C$", (8,0), S);[/asy]$

$\textbf{(E)}$ $[asy] size(75); pair A= (1.5,15) , B= (3,10) , C= (4.5,6) , D= (6,3) , E= (7.5,1) ; draw((0,-1)--(0,16)); draw((-1,0)--(16,0)); dot(A^^B^^C^^D^^E); label("$A$", (0,8), W); label("$C$", (8,0), S);[/asy]$

2007 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 15	Followed by Problem 17
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2007 AMC 8 Problems/Problem 16

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