Question

两个圆同心，半径分别为 $10$ 米和 $20$ 米。一只土豚沿图示路线奔跑，从 $A$ 出发，到 $K$ 结束。它跑了多少米？

Two circles that share the same center have radii $10$ meters and $20$ meters. An aardvark runs along the path shown, starting at $A$ and ending at $K.$ How many meters does the aardvark run?

$\ 10\pi+20$

$\ 10\pi+30$

$\ 10\pi+40$

$\ 20\pi+20$

$\ 20\pi+40$

答案：E

知识点：弧圆周长

难度评级：1380

解答：

圆的周长是 $\pi d = 2r\pi$ ，所以走四分之一圆周的长度是 $\dfrac {\pi r }2$ 。

它先沿大圆走四分之一圈，这部分是 $10 \pi$ 米。然后从大圆到小圆，长度为 $20-10=10$ 米。

接着沿小圆走四分之一圈，这部分是 $5 \pi$ 米。然后穿过小圆的直径，长度为 $10\cdot 2=20$ 米。

再沿小圆走四分之一圈，这部分是 $5 \pi$ 米。最后从小圆到大圆，长度为 $20-10=10$ 米。

总长度为 $10\pi + 10+5\pi + 20 + 5\pi + 10$ $=20\pi + 40.$

所以正确答案是 E。

The circumference of a circle is $\pi d = 2r\pi ,$ so going a quarter of the way around is $\dfrac {\pi r }2.$

He goes a quarter of the way around the large circle, so this part is $10 \pi$ meters. He then goes from the larger circle to the smaller circle, which is $20-10=10$ meters.

He goes a quarter of the way around the smaller circle, so this part is $5 \pi$ meters. He then goes through the diameter of the smaller circle, which is $10\cdot 2=20$ meters.

He then goes a quarter of the way around the smaller circle, so this part is $5 \pi$ meters. He finally goes from the smaller circle to the larger circle, which is $20-10=10$ meters.

The total length is $10\pi + 10+5\pi + 20 + 5\pi + 10$ $=20\pi + 40.$

Thus, the answer is E .

2008 AMC 8 第 18 题

答案：E

难度评级：1380

解答：

其他年份的第 18 题