AMC 8 2007 Problem 16
AMC8 2007 年第 16 题
表达式与运算★★★☆☆
Amanda 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?
Amanda 画了 5 个半径分别是 1，2，3，4 和 5 的圆。对于每个圆，她画了点（C，A），其中是这个园的周长，A 表示这个圆的面积。下面哪个可能是她画的图像？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
The circumferences of circles with radii 1 1 through 5 5 are 2 𝜋, 4 𝜋, 6 𝜋, 8 𝜋 2π,4π,6π,8π and 10 𝜋 10π, respectively. Their areas are, respectively, 𝜋, 4 𝜋, 9 𝜋, 16 𝜋 π,4π,9π,16π and 25 𝜋 25π. The points ( 2 𝜋, 𝜋 ), ( 4 𝜋, 4 𝜋 ), ( 6 𝜋, 9 𝜋 ), ( 8 𝜋, 16 𝜋 ) (2π,π),(4π,4π),(6π,9π),(8π,16π) and ( 10 𝜋, 25 𝜋 ) (10π,25π) are graphed in ( 𝐴 A). It is the only graph of an increasing quadratic function, called a parabola. Answer: 𝐴 A .
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