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比与比例

难度评级：1420

解答：

实际水塔的容量是迷你水塔的倍。这是体积比，所以高度比为因此迷你水塔的高度为米。 $\dfrac{100,000}{.1} = 1,000,000$ $(1,000,000)^{1 / 3} = 100.$ $\dfrac{40}{100} = .4.$

所以正确答案是 C。

The miniature tower holds $\dfrac{100,000}{.1} = 1,000,000$ times less water than the actual tower. Since this is the ratio for volumes, the ratio of heights is $(1,000,000)^{1 / 3} = 100.$ This means that the height of the miniature tower is $\dfrac{40}{100} = .4.$

Thus, C is the correct answer.

2010 AMC 10A 第 12 题

答案：C

难度评级：1420

解答：

其他年份的第 12 题