1952 AMC 12 第 1 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
1.
若一个圆的半径是有理数，则其面积是：
If the radius of a circle is a rational number, its area is given by a number which is:
有理数
Rational
无理数
Irrational
整数
Integral
完全平方数
A perfect square
以上答案均不正确
None of these
小提示：
用半径和 表示圆的面积
Write the area in terms of the radius and
大提示：
圆的半径为正数，所以这个有理数的平方不为零
A circle’s radius is positive, so its rational square is nonzero
解答：
若正有理数半径为 ，则圆的面积为 。因数 是非零有理数，而无理数 的非零有理数倍仍是无理数。
因此，正确答案是 B。
If the positive rational radius is then its area is The factor is a nonzero rational number, and a nonzero rational multiple of the irrational number is irrational.
Thus, the correct answer is B.
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