Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2006 AMC 8 Problems/Problem 7"

(Created page with "== Problem == Circle <math> X </math> has a radius of <math> \pi </math>. Circle <math> Y </math> has a circumference of <math> 8 \pi </math>. Circle <math> Z </math> has an are...")
 
(→‎Solution)
Line 7: Line 7:
 
== Solution ==
 
== Solution ==
  
−
Using the formulas of circles, <math> C=2 \pi r </math> and <math> A= \pi r^2 </math>. 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 <math> \boxed{\textbf{(B)}\ Z, X, Y} </math>.
+
Using the formulas of circles, <math> C=2 \pi r </math> and <math> A= \pi r^2 </math>, 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 <math> \boxed{\textbf{(B)}\ Z, X, Y} </math>.

Revision as of 20:43, 6 September 2011

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 $\boxed{\textbf{(B)}\ Z, X, Y}$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2006_AMC_8_Problems/Problem_7&oldid=42175"