Difference between revisions of "2007 AMC 12B Problems/Problem 19"
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| − | ==Problem | + | ==Problem== |
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>? | ||
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</asy> | </asy> | ||
| − | <math>V_{Cylinder} = \pi r^2 h</math> | + | <math>V_{\mathrm{Cylinder}} = \pi r^2 h</math> |
Where <math>C = 2\pi r = 6</math> and <math>h=6\sin\theta</math> | Where <math>C = 2\pi r = 6</math> and <math>h=6\sin\theta</math> | ||
Latest revision as of 15:35, 15 February 2021
Problem
Rhombus 
, with side length 
, is rolled to form a cylinder of volume by taping 
to 
. What is 
?
Solution
![[asy] pair B=(0,0), A=(6*dir(60)), C=(6,0); pair D=A+C; draw(A--B--C--D--A); draw(A--(3,0)); label("\(A\)",A,NW);label("\(B\)",B,SW);label("\(C\)",C,SE);label("\(D\)",D,NE); label("\(6\)",A/2,NW); label("\(\theta\)",(.8,.5)); label("\(h\)",(3,2.6),E); [/asy]](http://latex.artofproblemsolving.com/d/4/2/d423bf62199e5f6372de91d9c23fe0f39077413b.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 | |
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