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\text{ in } \times 2\text{ in } \times 1\text{ in}</math> blocks that can fit in a <math>3\text{ in | + | What is the largest number of solid <math>2\text{-in} \times 2\text{-in} \times 1\text{-in}</math> blocks that can fit in a <math>3\text{-in} \times 2\text{-in}\times3\text{-in}</math> box? |
<math>\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7</math> | <math>\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7</math> | ||
Revision as of 12:49, 16 February 2017
Problem
What is the largest number of solid 
blocks that can fit in a 
box?
Solution
We find that the volume of the larger block is 
, and the volume of the smaller block is 
. Dividing the two, we see that only a maximum of 
by by 
blocks can fit inside the 
by by block. Therefore, the answer is 
.
| 2017 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 AMC 10 Problems and Solutions | ||
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