Difference between revisions of "2011 AMC 8 Problems/Problem 25"

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filldraw((-1,0)--(0,1)--(1,0)--(0,-1)--cycle,white,black);</asy>
 
filldraw((-1,0)--(0,1)--(1,0)--(0,-1)--cycle,white,black);</asy>
  
<math> \text{(A)}\ \frac{1}2\qquad\text{(B)}\ 1\qquad\text{(C)}\ \frac{3}2\qquad\text{(D)}\ 2\qquad\text{(E)}\ \frac{5}2 </math>
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<math> \textbf{(A)}\ \frac{1}2\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ \frac{3}2\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \frac{5}2 </math>
  
 
==Solution==
 
==Solution==

Revision as of 19:26, 25 November 2011

Problem

A circle with radius $1$ is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?

[asy] filldraw((-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle,mediumgray,black); filldraw(Circle((0,0),1), mediumgray,black); filldraw((-1,0)--(0,1)--(1,0)--(0,-1)--cycle,white,black);[/asy]

$\textbf{(A)}\ \frac{1}2\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ \frac{3}2\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \frac{5}2$

Solution

See Also

2011 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 24
Followed by
Problem
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