2007 AMC 10A Problem 3

Problem 3 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 volume

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 these equal gives

4000h = 8000,

h = 2.

Thus, the correct answer is D.