Question

一个水族箱的长方形底面为 $100$ 厘米乘 $40$ 厘米，高为 $50$ 厘米。箱中水面高度为 $40$ 厘米。把一块底面为 $40$ 厘米乘 $20$ 厘米、高为 $10$ 厘米的长方体砖放入水族箱。水面会上升多少厘米？

An aquarium has a rectangular base that measures $100$ cm by $40$ cm and has a height of $50$ cm. It is filled with water to a height of $40$ cm. A brick with a rectangular base that measures $40$ cm by $20$ cm and a height of $10$ cm is placed in the aquarium. By how many centimeters does the water rise?

$0.5$

$1$

$1.5$

$2$

$2.5$

答案：D

知识点：体积长方体

难度评级：1020

小提示：

浸入水中的砖会排开与自身体积相同的水。

The submerged brick displaces its own volume of water

大提示：

水面上升高度等于砖的体积除以水族箱的底面积。

The rise equals the brick’s volume divided by the aquarium’s base area

解答：

砖的体积是 $40\cdot 20\cdot 10=8000$ 立方厘米。

如果水面上升 $h$ 厘米，增加的水体积是 $100\cdot 40\cdot h=4000h$ 立方厘米。

令它等于砖的体积，得 $8000=4000h$ ，所以 $h=2$ 。

因此，正确答案是 D。

The brick has a volume of $40\cdot 20\cdot 10=8000$ cubic centimeters.

If the water rises by $h$ centimeters, the added volume is $100\cdot 40\cdot h=4000h$ cubic centimeters.

Setting this equal to the brick’s volume gives $8000=4000h,$ so $h=2.$

Thus, the correct answer is D.

2007 AMC 12A 第 2 题

答案：D

难度评级：1020

小提示：

大提示：

解答：

其他年份的第 2 题