2007 AMC 12A Problem 2

Problem 2 of 25EasierGeometry

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?

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Solution

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,

h=2.

Thus, the correct answer is D.