AMC8 2006

AMC8 2006 · Q21

AMC8 2006 · Q21. It mainly tests Fractions, Area & perimeter.

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 cm³ is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?

一个水族箱有一个长方形底面，长100厘米，宽40厘米，高50厘米。水族箱中注水至37厘米深。然后放入一块体积为1000立方厘米的石头，完全浸没。问水位上升多少厘米？

(A) 0.25 0.25

(B) 0.5 0.5

(D) 1.25 1.25

(E) 2.5 2.5

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) Using the volume formula $lwh = V$, the volume of water in the aquarium is $100 \times 40 \times 37 = 148,000\ \text{cm}^3$. When the rock is put in, the water and the rock will occupy a box-shaped region with volume $148,000 + 1000 = 149,000\ \text{cm}^3$. The volume of the water and the rock is $100 \times 40 \times h$, where $h$ is the new height of the water. The new volume $= 4000h = 149,000\ \text{cm}^3$, so the new height is $$ h=\frac{149000}{4000}=37.25\ \text{cm}. $$ After adding the rock, the water rises $37.25 - 37 = 0.25\ \text{cm}$.

（A）使用体积公式 $lwh = V$，鱼缸中水的体积为 $100 \times 40 \times 37 = 148,000\ \text{cm}^3$。当把石头放入后，水和石头将占据一个长方体区域，其体积为 $148,000 + 1000 = 149,000\ \text{cm}^3$。水和石头的总体积为 $100 \times 40 \times h$，其中 $h$ 是水面新的高度。新的体积满足 $4000h = 149,000\ \text{cm}^3$，所以新的高度为 $$ h=\frac{149000}{4000}=37.25\ \text{cm}. $$ 加入石头后，水面上升 $37.25 - 37 = 0.25\ \text{cm}$。

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