1987 AMC 12 第 13 题

Question

一条宽

5

厘米的长纸带共绕

600

圈，所绕硬纸筒的直径为

2

厘米，最终形成直径为

10

厘米的收银机纸卷。估算纸带的长度（单位为米）。（把这张纸看成

600

个同心圆，其直径从

2

厘米到

10

厘米等间距排列。）

A long piece of paper

5

cm wide is made into a roll for cash registers by wrapping it

600

times around a cardboard tube of diameter

2

cm, forming a roll

10

cm in diameter. Approximate the length of the paper in meters. (Pretend the paper forms

600

concentric circles with diameters evenly spaced from

2

cm to

10

cm.)

36\pi

45\pi

60\pi

72\pi

90\pi

这

600

个直径组成一个等差数列

The

600

diameters form an arithmetic sequence

利用平均直径求出全部

600

个圆周长之和

Use the average diameter to find the sum of all

600

circumferences

首末直径的平均值为

\frac{2+10}{2}=6\text{ cm}\text{。}

因此，总长度约为

600(6\pi)=3600\pi

厘米，即

36\pi

米。

所以正确答案是 A。

The average of the first and last diameters is

\frac{2+10}{2}=6\text{ cm}.

Hence the total length is approximately

600(6\pi)=3600\pi

cm, or

36\pi

meters.

Thus the correct answer is A.

其他年份的第 13 题