2006 AMC 10B 第 4 题

Question

直径为

1

英寸和

3

英寸的两个圆同心。较小圆涂成红色，较小圆外且较大圆内的部分涂成蓝色。蓝色面积与红色面积之比是多少？

Circles of diameter

1

inch and

3

inches have the same center. The smaller circle is painted red, and the portion outside the smaller circle and inside the larger circle is painted blue. What is the ratio of the blue-painted area to the red-painted area?

2

3

6

8

9

答案：D

知识点：圆面积面积比

难度评级：940

小提示：

两个半径分别为

\tfrac12

和

\tfrac32

。

The radii are

\tfrac12

and

\tfrac32

大提示：

蓝色是圆环

\pi(\tfrac32)^2-\pi(\tfrac12)^2

；红色是

\pi(\tfrac12)^2

。

Blue is the ring

\pi(\tfrac32)^2-\pi(\tfrac12)^2

; red is

\pi(\tfrac12)^2

解答：

红色圆面积为

\pi(\tfrac12)^2 = \tfrac{\pi}{4}

，大圆面积为

\pi(\tfrac32)^2 = \tfrac{9\pi}{4}

。蓝色圆环面积为

\tfrac{9\pi}{4}-\tfrac{\pi}{4}=2\pi

。

因此蓝色面积是红色面积的

2\pi \div \tfrac{\pi}{4} = 8

倍。

所以正确答案是 D。

The red circle has area

\pi(\tfrac12)^2 = \tfrac{\pi}{4},

and the large circle has area

\pi(\tfrac32)^2 = \tfrac{9\pi}{4}.

The blue ring is

\tfrac{9\pi}{4}-\tfrac{\pi}{4}=2\pi.

The ratio is

2\pi \div \tfrac{\pi}{4} = 8.

Thus, the correct answer is D.

2006 AMC 10B 第 4 题

答案：D

难度评级：940

小提示：

大提示：

解答：

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