Question

Amanda Reckonwith 画了五个半径为 $1, 2, 3, 4$ 和 $5$ 的圆。然后对每个圆，她描点 $(C, A)$ ，其中 $C$ 是圆的周长， $A$ 是圆的面积。下列哪一个可能是她的图？

Amanda Reckonwith draws five circles with radii $1, 2, 3, 4$ and $5.$ Then for each circle she plots the point $(C, A),$ where $C$ is its circumference and $A$ is its area. Which of the following could be her graph?

答案：A

知识点：圆面积圆周长二次方程

难度评级：1400

解答：

半径 $1$ 到 $5$ 的圆的周长分别为 $2\pi,4\pi,6\pi,8\pi,10\pi$ ，对应面积为 $\pi,4\pi,9\pi,16\pi,25\pi$ 。

当 $C$ 等量增加时， $A$ 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 $1$ through $5$ are $2\pi,4\pi,6\pi,8\pi,10\pi$ . Their respective areas are $\pi,4\pi,9\pi,16\pi,25\pi$ .

As $C$ increases by equal amounts, $A$ 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.

2007 AMC 8 第 16 题

答案：A

难度评级：1400

解答：

其他年份的第 16 题