Difference between revisions of "2007 AMC 12A Problems/Problem 2"
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== Problem == | == Problem == | ||
| − | 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? | + | An aquarium has a [[rectangular prism|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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| + | <math>\mathrm{(A)}\ 0.5\qquad \mathrm{(B)}\ 1\qquad \mathrm{(C)}\ 1.5\qquad \mathrm{(D)}\ 2\qquad \mathrm{(E)}\ 2.5</math> | ||
== Solution == | == Solution == | ||
| − | The water has volume 100 | + | The water has volume <math>100 \cdot 40 \cdot 40=160000</math>. The brick has volume 8000. The water and the brick combined have a volume of 168000. The water rises |
| − | + | :<math>\frac{168000}{4000}-\frac{160000}{4000}=42-40=2</math> cm. | |
| + | == See also == | ||
| + | {{AMC12 box|year=2007|ab=A|num-b=1|num-a=3}} | ||
| − | + | [[Category:Introductory Algebra Problems]] | |
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Revision as of 10:40, 9 September 2007
Problem
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?
Solution
The water has volume 
. The brick has volume 8000. The water and the brick combined have a volume of 168000. The water rises
cm.
cm.See also
| 2007 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
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| All AMC 12 Problems and Solutions | |
