2010 AMC 8 第 16 题

Question

一个正方形和一个圆的面积相同。正方形边长与圆半径之比是多少？

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?

\ \dfrac{\sqrt{\pi}}{2}

\ \sqrt{\pi}

\ \pi

\ 2\pi

\ \pi^{2}

设

s^2=\pi r^2

，求

\frac{s}{r}

Set

s^2=\pi r^2

and solve for

\frac{s}{r}

.

分别用边长和半径表示正方形面积与圆面积

Write the square area and circle area in terms of side length and radius.

设正方形边长为

s

，圆半径为

r

。由于面积相同，

s^2 = \pi r^2

。因此

(\dfrac sr)^2 = \pi

，所以

\frac sr = \sqrt{ \pi}

。

所以正确答案是 B。

Let

s

be the side length of the square and let

r

be the radius of the circle. Then, since they have the same areas,

s^2 = \pi r^2 .

This means

(\dfrac sr)^2 = \pi,

so

\frac sr = \sqrt{ \pi} .

Thus, the answer is B .

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