2010 AMC 10A Problem 5 — Solution | LIVE by Po-Shen Loh

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2010 AMC 10A Problem 5

Below is the professionally curated solution for Problem 5 of the 2010 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 10A solutions, or check the answer key.

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Concepts:circumference circle area

Difficulty rating: 960

5.

The area of a circle whose circumference is $24\pi$ is $k\pi.$ What is the value of $k?$

$6$

$12$

$24$

$36$

$144$

Solution:

Recall that the formula for the circumference of a circle is $2 \pi r.$ We then have that $24\pi = 2\pi r$ $r = 12.$

The area of a circle is $\pi r^2,$ so we have that $k \pi = \pi 12^2$ $k = 144.$

Thus, E is the correct answer.

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