AMC 8 2010 Problem 16

AMC8 2010 年第 16 题

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A square and a circle have the same area. What is the ratio of the side length of the square to the radius of the circle?

一个正方形和一个圆有相同的面积。那么正方形的边长和圆的半径的比值是多少？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Let the side length of the square be

s

, and let the radius of the circle be

r

. Thus we have

s^2 = r^2\pi

. Dividing each side by

r^2

, we get

\displaystyle \frac{s^2}{r^2} = \pi

. Since

\displaystyle \left(\frac{s}{r}\right)^2 = \frac{s^2}{r^2}

, we have

\displaystyle \frac{s}{r} = \sqrt{\pi} \Rightarrow \sqrt{\pi}

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