Difference between revisions of "2010 AMC 10A Problems/Problem 5"

Revision as of 15:45, 20 December 2010

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

$\mathrm{(A)}\ 6 \qquad \mathrm{(B)}\ 12 \qquad \mathrm{(C)}\ 24 \qquad \mathrm{(D)}\ 36 \qquad \mathrm{(E)}\ 144$

If the circumference of a circle is $24\pi$ , the radius would be $12$ . Since the area of a circle is $\pi r^2$ , the area is $144\pi$ .

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+== Problem 5 ==
+The area of a circle whose circumference is <math>24\pi</math> is <math>k\pi</math>. What is the value of <math>k</math>?
+<math>
+\mathrm{(A)}\ 6
+\qquad
+\mathrm{(B)}\ 12
+\qquad
+\mathrm{(C)}\ 24
+\qquad
+\mathrm{(D)}\ 36
+\qquad
+\mathrm{(E)}\ 144
+</math>
+==Solution==
+If the circumference of a circle is <math>24\pi</math>, the radius would be <math>12</math>. Since the area of a circle is <math>\pi r^2</math>, the area is <math>144\pi</math>.