2001 AMC 12竞赛试题/第04题
Problem
Which of the cones listed below can be formed from a 
sector of a circle of radius 
by aligning the two straight sides?
![[asy] import graph; unitsize(1.5cm); defaultpen(fontsize(8pt)); draw(Arc((0,0),1,-72,180),linewidth(.8pt)); draw(dir(288)--(0,0)--(-1,0),linewidth(.8pt)); label(](/ueditor/php/upload/image/20180530/1527651318555040.png)
Solution
![[asy] import graph; unitsize(1.5cm); defaultpen(fontsize(8pt)); draw(Arc((0,0),1,-72,180),linewidth(.8pt) + red); draw(dir(288)--(0,0)--(-1,0),linewidth(.8pt) + blue); label(](/ueditor/php/upload/image/20180530/1527651326439427.png)
The blue lines will be joined together to form a single blue line on the surface of the cone, hence 
will be the 
of the cone.
The red line will form the circumference of the base. We can compute its length and use it to determine the radius.
The length of the red line is 
. This is the circumference of a circle with radius 
.
Therefore the correct answer is 
.
AEIS在线试听课程
