1986 AMC 12 第 18 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
18.
一个平面与半径为 的直圆柱相交，截面为椭圆。若椭圆的长轴比短轴长 ，则长轴的长度为
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
答案：E
小提示：
这种椭圆截面的短轴是圆柱的一条直径
The minor axis of such an elliptical section is a diameter of the cylinder
大提示：
将该直径增加 ，即可得到长轴
Increase that diameter by to obtain the major axis
解答：
直圆柱的椭圆平面截面的短轴是一条圆柱直径，因此其长度为 。长轴比它长 ，所以长轴的长度为
所以正确答案是 E。
The minor axis of an elliptical plane section of a right circular cylinder is a diameter of the cylinder. Its length is therefore The major axis is longer, so its length is
Thus the correct answer is E.
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