2017 AMC 10B Problems/Problem 6

Problem

What is the largest number of solid $2$ in x $2$ in x $1$ in blocks that can fit in a $3$ -in by $2$ in by $3$ 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
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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2017 AMC 10B Problems/Problem 6

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