2007 AMC 12A 第 2 题

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：

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