1951 AMC 12 第 10 题

Question

下列说法中，不正确的是：

Of the following statements, the one that is incorrect is:

将一个给定长方形的底边加倍，面积也加倍。

Doubling the base of a given rectangle doubles the area.

将三角形的高加倍，面积也加倍。

Doubling the altitude of a triangle doubles the area.

将一个给定圆的半径加倍，面积也加倍。

Doubling the radius of a given circle doubles the area.

将一个分式的除数加倍，并将其分子除以

2

，会改变商。

Doubling the divisor of a fraction and dividing its numerator by

2

changes the quotient.

将一个给定的量加倍，可能使结果小于原来的量。

Doubling a given quantity may make it less than it originally was.

检查各个面积公式在某个长度加倍时如何变化

Check how each area formula changes when one length is doubled

圆的面积取决于半径的平方

A circle’s area depends on the square of its radius

圆的面积为

\pi r^2

。将

r

替换为

2r

，得到

\pi(2r)^2=4\pi r^2

，所以半径加倍会使面积变为四倍，而不是两倍。其余说法按原文均可成立。

因此，正确答案是 C。

A circle has area

\pi r^2.

Replacing

r

by

2r

gives

\pi(2r)^2=4\pi r^2,

so doubling the radius quadruples, rather than doubles, the area. The other statements can hold as written.

Thus, the correct answer is C.

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