2008 AMC 8 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.
两个圆同心，半径分别为 米和 米。一只土豚沿图示路线奔跑，从 出发，到 结束。它跑了多少米？
Two circles that share the same center have radii meters and meters. An aardvark runs along the path shown, starting at and ending at How many meters does the aardvark run?
小提示：
把路线分成圆弧和直的径向线段
Break the route into circular arcs and straight radial segments.
大提示：
半径为 的四分之一圆弧长度为
A quarter-circle of radius has length .
解答：
圆的周长是 ，所以走四分之一圆周的长度是 。
它先沿大圆走四分之一圈，这部分是 米。然后从大圆到小圆，长度为 米。
接着沿小圆走四分之一圈，这部分是 米。然后穿过小圆的直径，长度为 米。
再沿小圆走四分之一圈，这部分是 米。最后从小圆到大圆，长度为 米。
总长度为
所以正确答案是 E。
The circumference of a circle is so going a quarter of the way around is
He goes a quarter of the way around the large circle, so this part is meters. He then goes from the larger circle to the smaller circle, which is meters.
He goes a quarter of the way around the smaller circle, so this part is meters. He then goes through the diameter of the smaller circle, which is meters.
He then goes a quarter of the way around the smaller circle, so this part is meters. He finally goes from the smaller circle to the larger circle, which is meters.
The total length is
Thus, the answer is E .
其他年份的第 18 题
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