AMC 8 2008 Problem 18

AMC8 2008 年第 18 题

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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?

两个同心圆的半径分别是 10 米和 20 米。一个土豚沿着图示路径运动，从 A 点开始到 K 点结束。则土豚总共运动了多少米？

A. $10\pi+20$
B. $10\pi+30$
C. $10\pi+40$
D. $20\pi+20$
E. $20\pi+40$

正确答案 · Correct Answer

解析 · Solution

Solution 1

We will deal with this part by part: Part 1:

\displaystyle \frac{1}{4}

circumference of big circle

\displaystyle = \frac{2\pi r}{4} = \frac{\pi r}{2} = \frac{20\pi}{2} = 10\pi

Part 2: Big radius minus small radius = 20-10=10 Part 3:

\displaystyle \frac{1}{4}

circumference of small circle

\displaystyle = \frac{\pi r}{2} = \frac{10\pi}{2} = 5\pi

Part 4: Diameter of small circle: 2*10=20 Part 5: Same as part 3:

5\pi

Part 6: Same as part 2: 10 Total:

10\pi + 10 + 5\pi + 20 + 5\pi + 10 = E = 20\pi + 40

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