2010 AMC 10A 第 5 题

Question

一个圆的周长为

24\pi

，其面积为

k\pi

。求

k

的值。

The area of a circle whose circumference is

24\pi

is

k\pi.

What is the value of

k?

6

12

24

36

144

先用周长求半径。

Use the circumference to find the radius first

由

2\pi r=24\pi

，所求

k

为

r^2

。

From

2\pi r=24\pi

, the desired

k

is

r^2

圆的周长公式为

2 \pi r

，所以

24\pi = 2\pi r

r = 12\text{。}

圆面积为

\pi r^2

，因此

k \pi = \pi 12^2

k = 144\text{。}

所以正确答案是 E。

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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