Difference between revisions of "2007 AMC 12B Problems/Problem 19"
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Rhombus <math>ABCD</math>, with side length <math>6</math>, is rolled to form a cylinder of volume <math>6</math> by taping <math>\overline{AB}</math> to <math>\overline{DC}</math>. What is <math>\sin(\angle ABC)</math>? | Rhombus <math>ABCD</math>, with side length <math>6</math>, is rolled to form a cylinder of volume <math>6</math> by taping <math>\overline{AB}</math> to <math>\overline{DC}</math>. What is <math>\sin(\angle ABC)</math>? | ||
| − | <math>\mathrm {(A)} \frac{\pi}{9} | + | <math>\mathrm{(A)}\ \frac{\pi}{9} \qquad \mathrm{(B)}\ \frac{1}{2} \qquad \mathrm{(C)}\ \frac{\pi}{6} \qquad \mathrm{(D)}\ \frac{\pi}{4} \qquad \mathrm{(E)}\ \frac{\sqrt{3}}{2}</math> |
==Solution== | ==Solution== | ||
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label("\(h\)",(3,2.6),E); | label("\(h\)",(3,2.6),E); | ||
</asy> | </asy> | ||
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<math>V_{Cylinder} = \pi r^2 h</math> | <math>V_{Cylinder} = \pi r^2 h</math> | ||
Revision as of 18:41, 28 March 2010
Problem 19
Rhombus 
, with side length 
, is rolled to form a cylinder of volume by taping 
to 
. What is 
?
Solution
![[asy] pair A=(0,0), B=(6*dir(60)), D=(6,0); pair C=B+D; draw(A--B--C--D--A); draw(B--(3,0)); label("\(A\)",A,SW);label("\(B\)",B,NW);label("\(C\)",C,NE);label("\(D\)",D,SE); label("\(6\)",B/2,NW); label("\(\theta\)",(.8,.5)); label("\(h\)",(3,2.6),E); [/asy]](http://latex.artofproblemsolving.com/a/4/9/a499cc3d755a90cb38c4d23013fdea50c737ba38.png)
Where 
and 
See Also
| 2007 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 18 |
Followed by Problem 20 |
| 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 AMC 12 Problems and Solutions | |
