AMC10 2006 B

AMC10 2006 B · Q4

AMC10 2006 B · Q4. It mainly tests Area & perimeter.

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?

直径分别为1英寸和3英寸的两个圆心相同。小圆涂成红色，大圆内小圆外的部分涂成蓝色。蓝色的面积与红色的面积之比是多少？

(A) 2 2

(B) 3 3

(D) 8 8

(E) 9 9

Answer

Correct choice: (D)

正确答案：（D）

Solution

The circle with diameter 3 has area $\pi (\frac{3}{2})^2$. The circle with diameter 1 has area $\pi (\frac{1}{2})^2$. Therefore the ratio of the blue-painted area to the red-painted area is $$\frac{\pi (\frac{3}{2})^2 - \pi (\frac{1}{2})^2}{\pi (\frac{1}{2})^2} = 8.$$

直径为3的圆面积为 $\pi (\frac{3}{2})^2$。直径为1的圆面积为 $\pi (\frac{1}{2})^2$。因此蓝色面积与红色面积之比为 $$\frac{\pi (\frac{3}{2})^2 - \pi (\frac{1}{2})^2}{\pi (\frac{1}{2})^2} = 8.$$

Topics

GE.007 Area & perimeter