AMC12 2007 A

AMC12 2007 A · Q2

AMC12 2007 A · Q2. It mainly tests Arithmetic misc, 3D geometry (volume).

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?

一个水族箱的底面是$100\text{ cm}\times 40\text{ cm}$的矩形，高$50\text{ cm}$。其中注水至$40\text{ cm}$高。将一块底面是$40\text{ cm}\times 20\text{ cm}$的矩形、高$10\text{ cm}$的砖块放入水族箱中。水位上升了多少厘米？

(A) 0.5 0.5

(B) 1 1

(D) 2 2

(E) 2.5 2.5

Answer

Correct choice: (D)

正确答案：（D）

Solution

The brick has volume $8000 cm^3$. The base of the aquarium has area $4000 cm^2$. For every cm the water rises, the volume increases by $4000 cm^3$; therefore, when the volume increases by $8000 cm^3$, the water level rises $2 cm \Rightarrow\fbox{D}$

砖块的体积为$8000 cm^3$。水族箱底面的面积为$4000 cm^2$。水位每上升$1$厘米，体积增加$4000 cm^3$；因此当体积增加$8000 cm^3$时，水位上升$2 cm \Rightarrow\fbox{D}$

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