Difference between revisions of "1986 AHSME Problems/Problem 18"
(Created page with "==Problem== A plane intersects a right circular cylinder of radius <math>1</math> forming an ellipse. If the major axis of the ellipse of <math>50\%</math> longer than the mino...") |
Robotman1717 (talk | contribs) m (→Problem) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 2: | Line 2: | ||
A plane intersects a right circular cylinder of radius <math>1</math> forming an ellipse. | A plane intersects a right circular cylinder of radius <math>1</math> forming an ellipse. | ||
| − | If the major axis of the ellipse | + | If the major axis of the ellipse is <math>50\%</math> longer than the minor axis, the length of the major axis is |
<math>\textbf{(A)}\ 1\qquad | <math>\textbf{(A)}\ 1\qquad | ||
| Line 8: | Line 8: | ||
\textbf{(C)}\ 2\qquad | \textbf{(C)}\ 2\qquad | ||
\textbf{(D)}\ \frac{9}{4}\qquad | \textbf{(D)}\ \frac{9}{4}\qquad | ||
| − | \textbf{(E)}\ 3 </math> | + | \textbf{(E)}\ 3 </math> |
==Solution== | ==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 <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 == | ||
Latest revision as of 18:31, 12 October 2023
Problem
A plane intersects a right circular cylinder of radius 
forming an ellipse.
If the major axis of the ellipse is 
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. 
