1978 AMC 12 第 2 题

Question

若某圆周长倒数的四倍等于该圆的直径，则这个圆的面积为

If four times the reciprocal of the circumference of a circle equals the diameter of the circle, then the area of the circle is

\frac1{\pi^2}

\frac1\pi

1

\pi

\pi^2

用半径

r

表示周长和直径

Write the circumference and diameter in terms of the radius

r

题设条件可以直接确定乘积

\pi r^2

The condition directly determines the product

\pi r^2

题设条件为

4\left(\frac1{2\pi r}\right)=2r\text{。}

两边乘以

\pi r

，得到

2=2\pi r^2

，所以面积

\pi r^2

等于

1

。

因此，正确答案是 C。

The condition is

4\left(\frac1{2\pi r}\right)=2r.

Multiplying by

\pi r

gives

2=2\pi r^2,

so the area

\pi r^2

equals

1.

Therefore, the correct answer is C.

其他年份的第 2 题