2017 AMC 10B Problems/Problem 6

Problem

What is the largest number of solid $2\text{in}$ by $2\text{in}$ by $1\text{in}$ blocks that can fit in a $3\text{in}$ by $2\text{in}$ by $3\text{in}$ box?

$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7$

Solution

By simply finding the volume of the larger block, we see that its area is $18$ . The volume of the smaller block is $4$ . Dividing the two, we see that only a maximum of $4$ $2$ in x $2$ in x $1$ in blocks can fit inside a $3$ -in by $2$ in by $3$ in box. $\qquad\textbf{(B)}\ 4$

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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2017 AMC 10B Problems/Problem 6

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