AMC10 2010 A

AMC10 2010 A · Q12

AMC10 2010 A · Q12. It mainly tests Ratios & proportions, 3D geometry (volume).

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?

Logan 正在制作他城镇的缩比模型。城市的水塔高 40 米，上部是一个容纳 100,000 升水的球体。Logan 的迷你水塔容纳 0.1 升水。Logan 应该把他的水塔做多高（米）？

(A) 0.04 0.04

(B) $\frac{0.4}{\pi}$ $\frac{0.4}{\pi}$

(D) $\frac{4}{\pi}$ $\frac{4}{\pi}$

(E) 4 4

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): The volume scale for Logan’s model is $0.1:100{,}000=1:1{,}000{,}000$. Therefore the linear scale is $1:\sqrt[3]{1{,}000{,}000}$, which is $1:100$. Logan’s water tower should stand $\dfrac{40}{100}=0.4$ meters tall.

答案（C）：Logan 模型的体积比例为 $0.1:100{,}000=1:1{,}000{,}000$。因此线性比例为 $1:\sqrt[3]{1{,}000{,}000}$，即 $1:100$。Logan 的水塔应为 $\dfrac{40}{100}=0.4$ 米高。

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