AMC 8 2006 Problem 21

AMC8 2006 年第 21 题

立体几何★★★☆☆

An aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. The aquarium is filled with water to a depth of 37 cm. A rock with volume

1000\text{cm}^3

is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?

一个鱼缸有一个尺寸为 100 厘米ｘ40 厘米的长方形底座，鱼缸高为 50 厘米。鱼缸里水深 37 厘米。将一块体积为 1000 立方厘米的石头放入鱼缸并完全浸没。问水位上升了多少厘米？

A.0.25
B.0.5
C.1
D.1.25
E.2.5

正确答案 · Correct Answer

解析 · Solution

Solution 1

The water level will rise 1 cm for every

100 \cdot 40 = 4000\text{ cm}^2

. Since 1000 is

\displaystyle \frac{1}{4}

of 4000, the water will rise

\displaystyle \frac{1}{4} \cdot 1 = 0.25

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