AMC8 2006

AMC8 2006 · Q7

AMC8 2006 · Q7. It mainly tests Area & perimeter.

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.

圆 X 的半径是 $\pi$。圆 Y 的周长是 $8\pi$。圆 Z 的面积是 $9\pi$。将这些圆按半径从小到大排序。

(A) X, Y, Z X, Y, Z

(B) Z, X, Y Z, X, Y

(D) Z, Y, X Z, Y, X

(E) X, Z, Y X, Z, Y

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) Because circumference $C = 2\pi r$ and circle $Y$ has circumference $8\pi$, its radius is $\frac{8\pi}{2\pi} = 4$. Because area $A = \pi r^2$ and circle $Z$ has area $9\pi$, its radius is $\sqrt{9} = 3$. Ordering the radii gives $3 < \pi < 4$, so the circles in ascending order of radii length are $Z$, $X$ and $Y$.

（B）因为周长 $C = 2\pi r$，且圆 $Y$ 的周长为 $8\pi$，所以它的半径是 $\frac{8\pi}{2\pi} = 4$。因为面积 $A = \pi r^2$，且圆 $Z$ 的面积为 $9\pi$，所以它的半径是 $\sqrt{9} = 3$。将半径大小排序得到 $3 < \pi < 4$，因此按半径从小到大排列的圆依次是 $Z$、$X$、$Y$。

Topics

GE.007 Area & perimeter