Question

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.

$X, Y, Z$

$Z, X, Y$

$Y, X, Z$

$Z, Y, X$

$X, Z, Y$

Answer: B

Concepts:circle circumference circle area

Difficulty rating: 960

Solution:

Recall that $C = 2 \pi r$ and $A = \pi r^2.$ Using these formulas we get that the radius of $Y$ is $8 \pi \div (2 \pi) = 4.$ We also get that the radius of $Z$ is $\sqrt{9 \pi \div \pi} = 3.$ As $\pi$ is greater than $3$ and less than $4,$ the correct order is $Z,X,Y.$

Thus, the answer is B .

2006 AMC 8 Problem 7

Answer: B

Difficulty rating: 960

Solution:

Problem 7 in Other Years