Difference between revisions of "2006 AMC 8 Problems/Problem 21"

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==Solution==
 
==Solution==
The water level will rise <math>1</math>cm for every <math>100 \cdot 40 = 4000\text{cm}^2</math>. Since <math>1000</math> is <math>\frac{1}{4}</math> of <math>4000</math>, the water will rise <math>\frac{1}{4}\cdot1 = \textbf{(A)}\ 0.25</math>
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The water level will rise <math>1</math>cm for every <math>100 \cdot 40 = 4000\text{cm}^2</math>. Since <math>1000</math> is <math>\frac{1}{4}</math> of <math>4000</math>, the water will rise <math>\frac{1}{4}\cdot1 = \boxed{\textbf{(A)}\ 0.25}</math>
  
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==See Also==
 
{{AMC8 box|year=2006|n=II|num-b=20|num-a=22}}
 
{{AMC8 box|year=2006|n=II|num-b=20|num-a=22}}
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{{MAA Notice}}

Latest revision as of 21:24, 7 January 2022

Problem

An aquarium has a rectangular base that measures $100$ cm by $40$ cm and has a height of $50$ cm. The aquarium is filled 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 $\frac{1}{4}\cdot1 = \boxed{\textbf{(A)}\ 0.25}$

See Also

2006 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
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 AJHSME/AMC 8 Problems and Solutions

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