AMC8 2008

AMC8 2008 · Q18

AMC8 2008 · Q18. It mainly tests Circle theorems, Area & perimeter.

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?

两个同心圆，半径分别为 $10$ 米和 $20$ 米。土豚沿着图示路径从 A 点跑到 K 点。土豚跑了多少米？

(A) $10\pi + 20$ $10\pi + 20$

(B) $10\pi + 30$ $10\pi + 30$

(D) $20\pi + 20$ $20\pi + 20$

(E) $20\pi + 40$ $20\pi + 40$

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): The length of first leg of the aardvark’s trip is $\frac{1}{4}(2\pi \times 20)=10\pi$ meters. The third and fifth legs are each $\frac{1}{4}(2\pi \times 10)=5\pi$ meters long. The second and sixth legs are each $10$ meters long, and the length of the fourth leg is $20$ meters. The length of the total trip is $10\pi+5\pi+5\pi+10+10+20=20\pi+40$ meters.

答案（E）：食蚁兽行程第一段的长度为 $\frac{1}{4}(2\pi \times 20)=10\pi$ 米。第三段和第五段的长度各为 $\frac{1}{4}(2\pi \times 10)=5\pi$ 米。第二段和第六段各为 $10$ 米，第四段的长度为 $20$ 米。全程长度为 $10\pi+5\pi+5\pi+10+10+20=20\pi+40$ 米。

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