2010 AMC 10A 第 12 题

Question

Logan 正在制作他的城镇的比例模型。该城市的水塔高

40

米，顶部是一个可容纳

100{,}000

升水的球体。Logan 的迷你水塔可容纳

0.1

升水。他应该把水塔做成多少米高？

Logan is constructing a scaled model of his town. The city’s water tower stands

40

meters high, and the top portion is a sphere that holds

100{,}000

liters of water. Logan’s miniature water tower holds

0.1

liters. How tall, in meters, should Logan make his tower?

0.04

\dfrac{0.4}{\pi}

0.4

\dfrac{4}{\pi}

4

体积比例是长度比例的立方。

Volume scale is the cube of length scale

比较

0.1

升和

100000

升，再取立方根。

Compare

0.1

liters to

100000

liters, then take a cube root

实际水塔的容量是迷你水塔的

\dfrac{100,000}{0.1} = 1,000,000

倍。这是体积比，所以高度比为

(1,000,000)^{\frac{1}{3}} = 100\text{。}

因此迷你水塔的高度为

\dfrac{40}{100} = 0.4\text{。}

所以正确答案是 C。

The miniature tower holds

\dfrac{100,000}{0.1} = 1,000,000

times less water than the actual tower. Since this is the ratio for volumes, the ratio of heights is

(1,000,000)^{\frac{1}{3}} = 100.

This means that the height of the miniature tower is

\dfrac{40}{100} = 0.4.

Thus, C is the correct answer.

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