2006 AMC 8 Problems/Problem 7

Problem

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.

$\textbf{(A)}\ X, Y, Z\qquad\textbf{(B)}\ Z, X, Y\qquad\textbf{(C)}\ Y, X, Z\qquad\textbf{(D)}\ Z, Y, X\qquad\textbf{(E)}\ X, Z, Y$

Solution

Using the formulas of circles, $C=2 \pi r$ and $A= \pi r^2$ . Therefore, circle Y has a radius of 4 and circle Z has a radius of 3. Thus, the order from smallest to largest radius is $\boxed{\textbf{(B)}\ Z, X, Y}$ .

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2006 AMC 8 Problems/Problem 7

Problem

Solution