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 | + | The brick has volume <math>8000 cm^3</math>. The base of the aquarium has area <math>4000 cm^2</math>. For every inch the water rises, the volume increases by <math>4000 cm^3</math>; therefore, when the volume increases by <math>8000 cm^3</math>, the water level rises <math>2 cm \Rightarrow\fbox{D}</math> |
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| + | == See also == | ||
| + | {{AMC12 box|year=2007|ab=A|num-b=1|num-a=3}} | ||
| − | + | [[Category:Introductory Algebra Problems]] | |
| − | + | {{MAA Notice}} | |
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Latest revision as of 20:30, 3 July 2013
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 brick has volume 
. The base of the aquarium has area 
. For every inch the water rises, the volume increases by 
; therefore, when the volume increases by , the water level rises 
See also
| 2007 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
