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2006 AMC 8 Problems/Problem 21

Revision as of 08:07, 18 December 2011 by AlcumusGuy (talk | contribs) (Created page with "==Problem== An aquarium has a rectangular base that measures <math>100</math> cm by <math>40</math> cm and has a height of <math>50</math> cm. The aquarium is tilled with water t...")
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Problem

An aquarium has a rectangular base that measures $100$ cm by $40$ cm and has a height of $50$ cm. The aquarium is tilled with water to a depth of $37$ cm. A rock with volume $1000\text{cm}^3$ is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?

$\textbf{(A)}\ 0.25\qquad\textbf{(B)}\ 0.5\qquad\textbf{(C)}\ 1\qquad\textbf{(D)}\ 1.25\qquad\textbf{(E)}\ 2.5$

Solution

The water level will rise $1$cm for every $100 \cdot 40 = 4000\text{cm}^2$. Since $1000$ is $\frac{1}{4}$ of $4000$, the water will rise $\frac{1}{4}\cdot1 = \textbf{(A)}\ 0.25$

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