AMC10 2007 A

AMC10 2007 A · Q3

AMC10 2007 A · Q3. It mainly tests 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?

一个水族箱底部是长 $100$ 厘米、宽 $40$ 厘米的矩形，高 $50$ 厘米。水族箱中注水至 $40$ 厘米高。将一块底部是 $40$ 厘米 $\times$ $20$ 厘米、高 $10$ 厘米的长方体砖放入水族箱中。水位上升多少厘米？

(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

Answer (D): The brick has a volume of $40\cdot 20\cdot 10=8000$ cubic centimeters. Suppose that after the brick is placed in the tank, the water level rises by $h$ centimeters. Then the additional volume occupied in the aquarium is $100\cdot 40\cdot h=4000h$ cubic centimeters. Since this must be the same as the volume of the brick, we have $8000=4000h$ and $h=2$ centimeters

答案（D）：砖块的体积为 $40\cdot 20\cdot 10=8000$ 立方厘米。假设砖块放入水箱后，水位上升 $h$ 厘米，则水族箱中新增所占体积为 $100\cdot 40\cdot h=4000h$ 立方厘米。由于这必须与砖块的体积相同，我们有 $8000=4000h$，因此 $h=2$ 厘米

Topics

GE.013 3D geometry (volume)