Question

圆 $X$ 的半径为 $\pi$ 。圆 $Y$ 的周长为 $8 \pi$ 。圆 $Z$ 的面积为 $9 \pi$ 。按半径从小到大排列这些圆。

Circle $X$ has a radius of $\pi.$ Circle $Y$ has a circumference of $8 \pi.$ Circle $Z$ has an area of $9 \pi.$ List the circles in order from smallest to largest radius.

$X, Y, Z$

$Z, X, Y$

$Y, X, Z$

$Z, Y, X$

$X, Z, Y$

答案：B

知识点：圆圆周长圆面积

难度评级：960

解答：

公式为 $C = 2 \pi r$ 和 $A = \pi r^2$ 。由此圆 $Y$ 的半径是 $8 \pi \div (2 \pi) = 4.$ 圆 $Z$ 的半径是 $\sqrt{9 \pi \div \pi} = 3.$ 因为 $\pi$ 大于 $3$ 且小于 $4$ ，所以正确顺序为 $Z,X,Y$ 。

所以正确答案是 B。

Recall that $C = 2 \pi r$ and $A = \pi r^2.$ Using these formulas we get that the radius of $Y$ is $8 \pi \div (2 \pi) = 4.$ We also get that the radius of $Z$ is $\sqrt{9 \pi \div \pi} = 3.$ As $\pi$ is greater than $3$ and less than $4,$ the correct order is $Z,X,Y.$

Thus, the answer is B .

2006 AMC 8 第 7 题

答案：B

难度评级：960

解答：

其他年份的第 7 题