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

m (Super Easy Solution)
(Solution)
Line 6: Line 6:
 
==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 = \boxed{\textbf{(A)}\ 0.25}</math>
 
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>
 +
 +
==Video Solution==
 +
 +
https://www.youtube.com/watch?v=DNMuW5prOwg
  
 
==See Also==
 
==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}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 15:18, 9 October 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 $\frac{1}{4}\cdot1 = \boxed{\textbf{(A)}\ 0.25}$

Video Solution

https://www.youtube.com/watch?v=DNMuW5prOwg

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png