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

AMC 8 2006 Problem 7

AMC8 2006 年第 7 题

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.

圆

X

的半径是

\pi

，圆

Y

的周长是

8\pi

，圆

Z

的面积是

9\pi

。将这三个圆按半径从小到大排序，正确的是？

正确答案 · Correct Answer

Solution 1

Not using the formulas of circles,

C=2 \pi r

and

A= \pi r^2

, we find that circle

Y

has a radius of 4 and circle

Z

has a radius of 3. Also, circle X has a radius of

\pi

. Thus, the order from smallest to largest radius is Z, X, Y.

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