AMC10 2010 A

AMC10 2010 A · Q5

AMC10 2010 A · Q5. It mainly tests Quadratic equations, Circle theorems.

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

周长为 $24\pi$ 的圆的面积是 $k\pi$。$k$ 的值为多少？

(A) 6 6

(B) 12 12

(D) 36 36

(E) 144 144

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): Because the circumference is $2\pi r = 24\pi$, the radius $r$ is 12. Therefore the area is $\pi r^2 = 144\pi$, and $k = 144$.

答案（E）：因为周长为 $2\pi r = 24\pi$，所以半径 $r$ 为 12。因此面积为 $\pi r^2 = 144\pi$，且 $k = 144$。

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