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?

$0.04$

$\dfrac{0.4}{\pi}$

$0.4$

$\dfrac{4}{\pi}$

$4$

答案：C

知识点：长度、面积与体积的缩放关系体积

难度评级：1420

解答：

模型与原物的体积比为 $\dfrac{0.1}{100{,}000}=\dfrac{1}{1{,}000{,}000}.$ 长度按体积比的立方根缩放，所以模型与原物的高度比为 $\dfrac1{100}.$ 因此模型的高度应为 $\dfrac{40}{100}=0.4$ 米。

所以正确答案是 C。

The model-to-original volume ratio is $\dfrac{0.1}{100{,}000}=\dfrac{1}{1{,}000{,}000}.$ Lengths scale by the cube root, so the model-to-original height ratio is $\dfrac1{100}.$ Therefore the model should be $\dfrac{40}{100}=0.4$ meters tall.

Thus, C is the correct answer.

2010 AMC 12A 第 7 题

答案：C

难度评级：1420

解答：

其他年份的第 7 题