1950 AMC 12 第 33 题

Question

内径为

1

英寸的圆管需要多少根，才能与一根内径为

6

英寸的圆管输送相同的水量？

The number of circular pipes with an inside diameter of

1

inch which will carry the same amount of water as a pipe with an inside diameter of

6

inches is:

6\pi

6

12

36

36\pi

输水能力与横截面积成正比

Water-carrying capacity is proportional to cross-sectional area

圆的面积与直径的平方成正比

Circular area scales as the square of the diameter

两种圆管的直径之比为

6:1

，所以横截面积之比为

6^2:1^2=36:1\text{。}

因此，

36

根小圆管的横截面积之和等于大圆管的横截面积。

因此，正确答案是 D。

The ratio of the diameters is

6:1,

so the ratio of cross-sectional areas is

6^2:1^2=36:1.

Thus

36

of the smaller pipes have the same total cross-sectional area as the larger pipe.

Thus, the correct answer is D.

其他年份的第 33 题