Difference between revisions of "2017 AMC 10B Problems/Problem 6"
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==Problem== | ==Problem== | ||
| − | + | What is the largest number of solid <math>2</math>in x<math>2</math>in x<math>1</math>in blocks that can fit in a <math>3</math>-in by <math>2</math> in by <math>3</math>in box? | |
| − | <math>\textbf{(A)}\ [ | + | <math>\textbf{(A)}\ [3]\qquad\textbf{(B)}\ [4]\qquad\textbf{(C)}\ [5]\qquad\textbf{(D)}\ [6]\qquad\textbf{(E)}\ [7]</math> |
==Solution== | ==Solution== | ||
| + | By simply finding the volume of the larger block, we see that its area is <math>18</math>. The volume of the smaller block is <math>4</math>. Dividing the two, we see that only a maximum of <math>4</math> <math>2</math>in x<math>2</math>in x<math>1</math>in blocks can fit inside a <math>3</math>-in by <math>2</math> in by <math>3</math>in box. <math>\qquad\textbf{(C)}\ [5]</math> | ||
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{{AMC10 box|year=2017|ab=b|num-b=5|num-a=7}} | {{AMC10 box|year=2017|ab=b|num-b=5|num-a=7}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 08:22, 16 February 2017
Problem
What is the largest number of solid 
in xin x
in blocks that can fit in a 
-in by in by in box?
![$\textbf{(A)}\ [3]\qquad\textbf{(B)}\ [4]\qquad\textbf{(C)}\ [5]\qquad\textbf{(D)}\ [6]\qquad\textbf{(E)}\ [7]$](http://latex.artofproblemsolving.com/5/4/e/54ef60c83d0d761bb8b14c185a3629b9d7a28700.png)
Solution
By simply finding the volume of the larger block, we see that its area is 
. The volume of the smaller block is 
. Dividing the two, we see that only a maximum of in xin xin blocks can fit inside a -in by in by in box. ![$\qquad\textbf{(C)}\ [5]$](http://latex.artofproblemsolving.com/2/2/6/226a56f8da12c16aeed77ed5fbb86859f271719b.png)
| 2017 AMC 10b (Problems • Answer Key • Resources) | ||
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Followed by Problem 7 | |
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