Difference between revisions of "1986 AHSME Problems/Problem 18"
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| + | We note that we can draw the minor axis to see that because the minor axis is the minimum distance between two opposite points on the ellipse, we can draw a line through two opposite points of the cylinder, and so the minor axis is <math>2(1) = 2</math>. Therefore, our answer is <math>2(1.5) = 3</math>, and so our answer is <math>\boxed{E}</math>. | ||
== See also == | == See also == | ||
Revision as of 19:01, 9 October 2017
Problem
A plane intersects a right circular cylinder of radius 
forming an ellipse.
If the major axis of the ellipse of 
longer than the minor axis, the length of the major axis is
Solution
We note that we can draw the minor axis to see that because the minor axis is the minimum distance between two opposite points on the ellipse, we can draw a line through two opposite points of the cylinder, and so the minor axis is 
. Therefore, our answer is 
, and so our answer is 
.
See also
| 1986 AHSME (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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
