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 xin blocks that can fit in a -in by in by in box?
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.
2017 AMC 10b (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AMC 10 Problems and Solutions |
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