2007 AMC 8 第 16 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。
16.
Amanda Reckonwith 画了五个半径为 、、、 和 的圆。然后对每个圆，她描点 ，其中 是圆的周长， 是圆的面积。下列哪一个可能是她的图？
Amanda Reckonwith draws five circles with radii and Then for each circle she plots the point where is its circumference and is its area. Which of the following could be her graph?
小提示：
用半径表示周长和面积
Write circumference and area in terms of the radius.
大提示：
当周长随半径线性增长时，面积随半径平方增长
As the circumference grows linearly with radius, the area grows quadratically.
解答：
半径 到 的圆的周长分别为 、、、 和 ，对应面积分别为 、、、 和 。
当 等量增加时， 增加得越来越快，所以这些点形成递增的二次形状。只有图 A 有这种形状。
所以正确答案是 A。
The circumferences of circles with radii through are and . Their respective areas are and .
As increases by equal amounts, increases more and more quickly, so the points form an increasing quadratic pattern. Only graph A has that shape.
Thus, A is the correct answer.
其他年份的第 16 题
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