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

See Also

2006 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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All AJHSME/AMC 8 Problems and Solutions

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